1.
Electromagnetism
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Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force usually exhibits electromagnetic fields such as fields, magnetic fields. The other three fundamental interactions are the interaction, the weak interaction, and gravitation. The word electromagnetism is a form of two Greek terms, ἤλεκτρον, ēlektron, amber, and μαγνῆτις λίθος magnētis lithos, which means magnesian stone. The electromagnetic force plays a role in determining the internal properties of most objects encountered in daily life. Ordinary matter takes its form as a result of forces between individual atoms and molecules in matter, and is a manifestation of the electromagnetic force. Electrons are bound by the force to atomic nuclei, and their orbital shapes. The electromagnetic force governs the processes involved in chemistry, which arise from interactions between the electrons of neighboring atoms, there are numerous mathematical descriptions of the electromagnetic field. In classical electrodynamics, electric fields are described as electric potential, although electromagnetism is considered one of the four fundamental forces, at high energy the weak force and electromagnetic force are unified as a single electroweak force. In the history of the universe, during the epoch the unified force broke into the two separate forces as the universe cooled. Originally, electricity and magnetism were considered to be two separate forces, Magnetic poles attract or repel one another in a manner similar to positive and negative charges and always exist as pairs, every north pole is yoked to a south pole. An electric current inside a wire creates a corresponding magnetic field outside the wire. Its direction depends on the direction of the current in the wire. A current is induced in a loop of wire when it is moved toward or away from a field, or a magnet is moved towards or away from it. While preparing for a lecture on 21 April 1820, Hans Christian Ørsted made a surprising observation. As he was setting up his materials, he noticed a compass needle deflected away from north when the electric current from the battery he was using was switched on. At the time of discovery, Ørsted did not suggest any explanation of the phenomenon. However, three later he began more intensive investigations
2.
Electricity
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Electricity is the set of physical phenomena associated with the presence of electric charge. Although initially considered a separate to magnetism, since the development of Maxwells Equations both are recognized as part of a single phenomenon, electromagnetism. Various common phenomena are related to electricity, including lightning, static electricity, electric heating, electric discharges, in addition, electricity is at the heart of many modern technologies. The presence of a charge, which can be either positive or negative. On the other hand, the movement of charges, which is known as electric current. When a charge is placed in a location with non-zero electric field, the magnitude of this force is given by Coulombs Law. Thus, if that charge were to move, the field would be doing work on the electric charge. Electrical phenomena have been studied since antiquity, though progress in theoretical understanding remained slow until the seventeenth and eighteenth centuries. Even then, practical applications for electricity were few, and it would not be until the nineteenth century that engineers were able to put it to industrial and residential use. The rapid expansion in electrical technology at this time transformed industry, electricitys extraordinary versatility means it can be put to an almost limitless set of applications which include transport, heating, lighting, communications, and computation. Electrical power is now the backbone of modern industrial society, long before any knowledge of electricity existed, people were aware of shocks from electric fish. Ancient Egyptian texts dating from 2750 BCE referred to these fish as the Thunderer of the Nile, Electric fish were again reported millennia later by ancient Greek, Roman and Arabic naturalists and physicians. Patients suffering from such as gout or headache were directed to touch electric fish in the hope that the powerful jolt might cure them. Ancient cultures around the Mediterranean knew that certain objects, such as rods of amber, Thales was incorrect in believing the attraction was due to a magnetic effect, but later science would prove a link between magnetism and electricity. He coined the New Latin word electricus to refer to the property of attracting small objects after being rubbed and this association gave rise to the English words electric and electricity, which made their first appearance in print in Thomas Brownes Pseudodoxia Epidemica of 1646. Further work was conducted by Otto von Guericke, Robert Boyle, Stephen Gray, in the 18th century, Benjamin Franklin conducted extensive research in electricity, selling his possessions to fund his work. In June 1752 he is reputed to have attached a key to the bottom of a dampened kite string. A succession of jumping from the key to the back of his hand showed that lightning was indeed electrical in nature
3.
Magnetism
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Magnetism is a class of physical phenomena that are mediated by magnetic fields. Electric currents and the moments of elementary particles give rise to a magnetic field. The most familiar effects occur in materials, which are strongly attracted by magnetic fields and can be magnetized to become permanent magnets. Only a few substances are ferromagnetic, the most common ones are iron, nickel and cobalt, the prefix ferro- refers to iron, because permanent magnetism was first observed in lodestone, a form of natural iron ore called magnetite, Fe3O4. The magnetic state of a material depends on temperature and other such as pressure. A material may exhibit more than one form of magnetism as these variables change, magnetism was first discovered in the ancient world, when people noticed that lodestones, naturally magnetized pieces of the mineral magnetite, could attract iron. The word magnet comes from the Greek term for lodestone, magnítis líthos, in ancient Greece, Aristotle attributed the first of what could be called a scientific discussion of magnetism to the philosopher Thales of Miletus, who lived from about 625 BC to about 545 BC. Around the same time, in ancient India, the Indian surgeon Sushruta was the first to use of the magnet for surgical purposes. In ancient China, the earliest literary reference to magnetism lies in a 4th-century BC book named after its author, the 2nd-century BC annals, Lüshi Chunqiu, also notes, The lodestone makes iron approach, or it attracts it. The earliest mention of the attraction of a needle is in a 1st-century work Lunheng, by the 12th century the Chinese were known to use the lodestone compass for navigation. They sculpted a directional spoon from lodestone in such a way that the handle of the spoon always pointed south, alexander Neckam, by 1187, was the first in Europe to describe the compass and its use for navigation. In 1269, Peter Peregrinus de Maricourt wrote the Epistola de magnete, in 1282, the properties of magnets and the dry compass were discussed by Al-Ashraf, a Yemeni physicist, astronomer, and geographer. In 1600, William Gilbert published his De Magnete, Magneticisque Corporibus, in this work he describes many of his experiments with his model earth called the terrella. From his experiments, he concluded that the Earth was itself magnetic and this landmark experiment is known as Ørsteds Experiment. James Clerk Maxwell synthesized and expanded these insights into Maxwells equations, unifying electricity, magnetism, in 1905, Einstein used these laws in motivating his theory of special relativity, requiring that the laws held true in all inertial reference frames. Magnetism, at its root, arises from two sources, Electric current, Spin magnetic moments of elementary particles. The magnetic moments of the nuclei of atoms are thousands of times smaller than the electrons magnetic moments. Nuclear magnetic moments are very important in other contexts, particularly in nuclear magnetic resonance
4.
Electrostatics
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Electrostatics is a branch of physics that deals with the phenomena and properties of stationary or slow-moving electric charges. Since classical physics, it has known that some materials such as amber attract lightweight particles after rubbing. The Greek word for amber, ήλεκτρον, or electron, was the source of the word electricity, Electrostatic phenomena arise from the forces that electric charges exert on each other. Such forces are described by Coulombs law, Electrostatics involves the buildup of charge on the surface of objects due to contact with other surfaces. This is because the charges that transfer are trapped there for a long enough for their effects to be observed. We begin with the magnitude of the force between two point charges q and Q. It is convenient to one of these charges, q, as a test charge. As we develop the theory, more source charges will be added.854187817 ×10 −12 C2 N −1 m −2, the SI units of ε0 are equivalently A2s4 kg−1m−3 or C2N−1m−2 or F m−1. Coulombs constant is, k e ≈14 π ε0 ≈8.987551787 ×109 N m 2 C −2. A single proton has a charge of e, and the electron has a charge of −e and these physical constants are currently defined so that ε0 and k0 are exactly defined, and e is a measured quantity. Electric field lines are useful for visualizing the electric field, field lines begin on positive charge and terminate on negative charge. Electric field lines are parallel to the direction of the field. The electric field, E →, is a field that can be defined everywhere. It is convenient to place a hypothetical test charge at a point, by Coulombs Law, this test charge will experience a force that can be used to define the electric field as follow F → = q E →. For a single point charge at the origin, the magnitude of electric field is E = k e Q / R2. The fact that the force can be calculated by summing all the contributions due to individual source particles is an example of the superposition principle. If the charge is distributed over a surface or along a line, the Divergence Theorem allows Gausss Law to be written in differential form, ∇ → ⋅ E → = ρ ε0. Where ∇ → ⋅ is the divergence operator, the definition of electrostatic potential, combined with the differential form of Gausss law, provides a relationship between the potential Φ and the charge density ρ, ∇2 ϕ = − ρ ε0
5.
Electric charge
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Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of charges, positive and negative. Like charges repel and unlike attract, an absence of net charge is referred to as neutral. An object is charged if it has an excess of electrons. The SI derived unit of charge is the coulomb. In electrical engineering, it is common to use the ampere-hour. The symbol Q often denotes charge, early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that dont require consideration of quantum effects. The electric charge is a conserved property of some subatomic particles. Electrically charged matter is influenced by, and produces, electromagnetic fields, the interaction between a moving charge and an electromagnetic field is the source of the electromagnetic force, which is one of the four fundamental forces. 602×10−19 coulombs. The proton has a charge of +e, and the electron has a charge of −e, the study of charged particles, and how their interactions are mediated by photons, is called quantum electrodynamics. Charge is the property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter. Electric charge is a property of many subatomic particles. The charges of free-standing particles are integer multiples of the charge e. Michael Faraday, in his electrolysis experiments, was the first to note the discrete nature of electric charge, robert Millikans oil drop experiment demonstrated this fact directly, and measured the elementary charge. By convention, the charge of an electron is −1, while that of a proton is +1, charged particles whose charges have the same sign repel one another, and particles whose charges have different signs attract. The charge of an antiparticle equals that of the corresponding particle, quarks have fractional charges of either −1/3 or +2/3, but free-standing quarks have never been observed. The electric charge of an object is the sum of the electric charges of the particles that make it up. An ion is an atom that has lost one or more electrons, giving it a net charge, or that has gained one or more electrons
6.
Static electricity
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Static electricity is an imbalance of electric charges within or on the surface of a material. The charge remains until it is able to move away by means of a current or electrical discharge. Static electricity is named in contrast with current electricity, which flows through wires or other conductors, a static electric charge can be created whenever two surfaces contact and separate, and at least one of the surfaces has a high resistance to electric current. The familiar phenomenon of a static shock–more specifically, an electrostatic discharge–is caused by the neutralization of charge, materials are made of atoms that are normally electrically neutral because they contain equal numbers of positive charges and negative charges. The phenomenon of static electricity requires a separation of positive and negative charges, when two materials are in contact, electrons may move from one material to the other, which leaves an excess of positive charge on one material, and an equal negative charge on the other. When the materials are separated they retain this charge imbalance and this is known as the triboelectric effect and results in one material becoming positively charged and the other negatively charged. The polarity and strength of the charge on a material once they are separated depends on their positions in the triboelectric series. The triboelectric effect is the cause of static electricity as observed in everyday life. Contact-induced charge separation causes your hair to stand up and causes static cling, pressure-induced charge separation Applied mechanical stress generates a separation of charge in certain types of crystals and ceramics molecules. Heat-induced charge separation Heating generates a separation of charge in the atoms or molecules of certain materials, all pyroelectric materials are also piezoelectric. The atomic or molecular properties of heat and pressure response are closely related, charge-induced charge separation A charged object brought close to an electrically neutral object causes a separation of charge within the neutral object. Charges of the same polarity are repelled and charges of the opposite polarity are attracted, as the force due to the interaction of electric charges falls off rapidly with increasing distance, the effect of the closer charges is greater and the two objects feel a force of attraction. The effect is most pronounced when the object is an electrical conductor as the charges are more free to move around. Careful grounding of part of an object with a charge separation can permanently add or remove electrons, leaving the object with a global. This process is integral to the workings of the Van de Graaff generator, removing or preventing a buildup of static charge can be as simple as opening a window or using a humidifier to increase the moisture content of the air, making the atmosphere more conductive. Air ionizers can perform the same task, fabric softeners and dryer sheets used in washing machines and clothes dryers are an example of an antistatic agent used to prevent and remove static cling. Many semiconductor devices used in electronics are particularly sensitive to static discharge, conductive antistatic bags are commonly used to protect such components. People who work on circuits that contain these devices often ground themselves with an antistatic strap
7.
Electric field
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An electric field is a vector field that associates to each point in space the Coulomb force that would be experienced per unit of electric charge, by an infinitesimal test charge at that point. Electric fields are created by electric charges and can be induced by time-varying magnetic fields, the electric field combines with the magnetic field to form the electromagnetic field. The electric field, E, at a point is defined as the force, F. A particle of charge q would be subject to a force F = q E and its SI units are newtons per coulomb or, equivalently, volts per metre, which in terms of SI base units are kg⋅m⋅s−3⋅A−1. Electric fields are caused by electric charges or varying magnetic fields, in the special case of a steady state, the Maxwell-Faraday inductive effect disappears. The resulting two equations, taken together, are equivalent to Coulombs law, written as E =14 π ε0 ∫ d r ′ ρ r − r ′ | r − r ′ |3 for a charge density ρ. Notice that ε0, the permittivity of vacuum, must be substituted if charges are considered in non-empty media, the equations of electromagnetism are best described in a continuous description. A charge q located at r 0 can be described mathematically as a charge density ρ = q δ, conversely, a charge distribution can be approximated by many small point charges. Electric fields satisfy the principle, because Maxwells equations are linear. This principle is useful to calculate the field created by point charges. Q n are stationary in space at r 1, r 2, in that case, Coulombs law fully describes the field. If a system is static, such that magnetic fields are not time-varying, then by Faradays law, in this case, one can define an electric potential, that is, a function Φ such that E = − ∇ Φ. This is analogous to the gravitational potential, Coulombs law, which describes the interaction of electric charges, F = q = q E is similar to Newtons law of universal gravitation, F = m = m g. This suggests similarities between the electric field E and the gravitational field g, or their associated potentials, mass is sometimes called gravitational charge because of that similarity. Electrostatic and gravitational forces both are central, conservative and obey an inverse-square law, a uniform field is one in which the electric field is constant at every point. It can be approximated by placing two conducting plates parallel to other and maintaining a voltage between them, it is only an approximation because of boundary effects. Assuming infinite planes, the magnitude of the electric field E is, electrodynamic fields are E-fields which do change with time, for instance when charges are in motion. The electric field cannot be described independently of the field in that case
8.
Electrical conductor
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In physics and electrical engineering, a conductor is an object or type of material that allows the flow of an electrical current in one or more directions. Materials made of metal are common electrical conductors, Electrical current is generated by the flow of negatively charged electrons, positively charged holes, and positive or negative ions in some cases. In order for current to flow, it is not necessary for one charged particle to travel from the producing the current to that consuming it. Instead, the particle simply needs to nudge its neighbor a finite amount who will nudge its neighbor and on and on until a particle is nudged into the consumer. Essentially what is occurring here is a chain of momentum transfer between mobile charge carriers, the Drude model of conduction describes this process more rigorously. Insulators are non-conducting materials with few mobile charges that support only insignificant electric currents, the resistance of a given conductor depends on the material it is made of, and on its dimensions. For a given material, the resistance is proportional to the cross-sectional area. For example, a copper wire has lower resistance than an otherwise-identical thin copper wire. Also, for a material, the resistance is proportional to the length, for example. The resistance R and conductance G of a conductor of uniform cross section, therefore, the resistivity and conductivity are proportionality constants, and therefore depend only on the material the wire is made of, not the geometry of the wire. Resistivity and conductivity are reciprocals, ρ =1 / σ, resistivity is a measure of the materials ability to oppose electric current. This formula is not exact, It assumes the current density is uniform in the conductor. However, this still provides a good approximation for long thin conductors such as wires. Another situation this formula is not exact for is with alternating current, then, the geometrical cross-section is different from the effective cross-section in which current actually flows, so the resistance is higher than expected. Similarly, if two conductors are each other carrying AC current, their resistances increase due to the proximity effect. Aside from the geometry of the wire, temperature also has a significant effect on the efficacy of conductors, temperature affects conductors in two main ways, the first is that materials may expand under the application of heat. The amount that the material will expand is governed by the expansion coefficient specific to the material. Such an expansion will change the geometry of the conductor and therefore its characteristic resistance, however, this effect is generally small, on the order of 10−6
9.
Insulator (electricity)
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An electrical insulator is a material whose internal electric charges do not flow freely, very little electric current will flow through it under the influence of an electric field. This contrasts with other materials, semiconductors and conductors, which conduct electric current more easily, the property that distinguishes an insulator is its resistivity, insulators have higher resistivity than semiconductors or conductors. A perfect insulator does not exist, because even insulators contain small numbers of mobile charges which can carry current, in addition, all insulators become electrically conductive when a sufficiently large voltage is applied that the electric field tears electrons away from the atoms. This is known as the voltage of an insulator. Some materials such as glass, paper and Teflon, which have high resistivity, are good electrical insulators. Examples include rubber-like polymers and most plastics which can be thermoset or thermoplastic in nature, insulators are used in electrical equipment to support and separate electrical conductors without allowing current through themselves. An insulating material used in bulk to wrap electrical cables or other equipment is called insulation, the term insulator is also used more specifically to refer to insulating supports used to attach electric power distribution or transmission lines to utility poles and transmission towers. They support the weight of the suspended wires without allowing the current to flow through the tower to ground, electrical insulation is the absence of electrical conduction. Electronic band theory says that a charge flows if states are available into which electrons can be excited and this allows electrons to gain energy and thereby move through a conductor such as a metal. If no such states are available, the material is an insulator, most insulators have a large band gap. This occurs because the valence band containing the highest energy electrons is full, there is always some voltage that gives electrons enough energy to be excited into this band. Once this voltage is exceeded the material ceases being an insulator, however, it is usually accompanied by physical or chemical changes that permanently degrade the materials insulating properties. Materials that lack electron conduction are insulators if they lack other mobile charges as well, for example, if a liquid or gas contains ions, then the ions can be made to flow as an electric current, and the material is a conductor. Electrolytes and plasmas contain ions and act as conductors whether or not electron flow is involved, when subjected to a high enough voltage, insulators suffer from the phenomenon of electrical breakdown. These freed electrons and ions are in turn accelerated and strike other atoms, creating more charge carriers, rapidly the insulator becomes filled with mobile charge carriers, and its resistance drops to a low level. In a solid, the voltage is proportional to the band gap energy. The air in a region around a conductor can break down and ionise without a catastrophic increase in current. Even a vacuum can suffer a sort of breakdown, but in case the breakdown or vacuum arc involves charges ejected from the surface of metal electrodes rather than produced by the vacuum itself
10.
Triboelectric effect
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The triboelectric effect is a type of contact electrification in which certain materials become electrically charged after they come into frictional contact with a different material. Rubbing glass with fur, or a plastic comb through the hair, most everyday static electricity is triboelectric. The polarity and strength of the charges produced differ according to the materials, surface roughness, temperature, strain, the triboelectric effect is not very predictable, and only broad generalizations can be made. Amber, for example, can acquire a charge by contact. This property was first recorded by Thales of Miletus, the word electricity is derived from William Gilberts initial coinage, electra, which originates in the Greek word for amber, ēlektron. The prefix tribo- refers to ‘friction’, as in tribology, other examples of materials that can acquire a significant charge when rubbed together include glass rubbed with silk, and hard rubber rubbed with fur. Physical separation of materials that are adhered together results in friction between the materials, thus, a material can develop a positive or negative charge that dissipates after the materials separate. Johan Carl Wilcke published the first triboelectric series in a 1757 paper on static charges, materials are often listed in order of the polarity of charge separation when they are touched with another object. A material towards the bottom of the series, when touched to a material near the top of the series, the farther away two materials are from each other on the series, the greater the charge transferred. Materials near to other on the series may not exchange any charge. This can be caused by rubbing, by contaminants or oxides, lists vary somewhat as to the exact order of some materials, since the relative charge varies for nearby materials. From actual tests, there is little or no difference in charge affinity between metals, probably because the rapid motion of conduction electrons cancels such differences. Although the part tribo- comes from the Greek for rubbing, τρίβω, after coming into contact, a chemical bond is formed between parts of the two surfaces, called adhesion, and charges move from one material to the other to equalize their electrochemical potential. This is what creates the net imbalance between the objects. In addition, some materials may exchange ions of differing mobility, the triboelectric effect is related to friction only because they both involve adhesion. However, the effect is enhanced by rubbing the materials together, as they touch. Surface nano-effects are not well understood, and the atomic force microscope has enabled rapid progress in this field of physics, a person simply walking across a carpet may build up a potential of many thousands of volts, enough to cause a spark one centimeter long or more. Simply removing a nylon shirt or corset can also create sparks, car travel can lead to a build-up of charge on the driver and passengers due to friction between the drivers clothes and the leather or plastic furnishings inside the vehicle
11.
Electrostatic discharge
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Electrostatic discharge is the sudden flow of electricity between two electrically charged objects caused by contact, an electrical short, or dielectric breakdown. A buildup of static electricity can be caused by tribocharging or by electrostatic induction, the ESD occurs when differently-charged objects are brought close together or when the dielectric between them breaks down, often creating a visible spark. ESD can create electric sparks, but also less dramatic forms which may be neither seen nor heard. Electric sparks require a field strength above approximately 40 kV/cm in air, other forms of ESD include corona discharge from sharp electrodes and brush discharge from blunt electrodes. These can suffer permanent damage when subjected to high voltages, ESD simulators may be used to test electronic devices, for example with a human body model or a charged device model. One of the causes of ESD events is static electricity, static electricity is often generated through tribocharging, the separation of electric charges that occurs when two materials are brought into contact and then separated. In all these cases, the breaking of contact between two materials results in tribocharging, thus creating a difference of potential that can lead to an ESD event. Another cause of ESD damage is through electrostatic induction and this occurs when an electrically charged object is placed near a conductive object isolated from the ground. The presence of the object creates an electrostatic field that causes electrical charges on the surface of the other object to redistribute. Even though the net charge of the object has not changed. An ESD event may occur when the object comes into contact with a conductive path, ESD can also be caused by energetic charged particles impinging on an object. This causes increasing surface and deep charging and this is a known hazard for most spacecraft. The most spectacular form of ESD is the spark, which occurs when an electric field creates an ionized conductive channel in air. This can cause discomfort to people, severe damage to electronic equipment. However, many ESD events occur without a visible or audible spark, a person carrying a relatively small electric charge may not feel a discharge that is sufficient to damage sensitive electronic components. Some devices may be damaged by discharges as small as 30V and these invisible forms of ESD can cause outright device failures, or less obvious forms of degradation that may affect the long term reliability and performance of electronic devices. The degradation in some devices may not become evident until well into their service life, a spark is triggered when the electric field strength exceeds approximately 4–30 kV/cm — the dielectric field strength of air. Perhaps the best known example of a spark is lightning
12.
Electrostatic induction
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In the presence of a charged body, an insulated conductor develops a positive charge on one end and a negative charge on the other end. Induction was discovered by British scientist John Canton in 1753 and Swedish professor Johan Carl Wilcke in 1762, electrostatic generators, such as the Wimshurst machine, the Van de Graaff generator and the electrophorus, use this principle. Due to induction, the potential is constant at any point throughout a conductor. Electrostatic Induction is also responsible for the attraction of light objects, such as balloons, paper or styrofoam scraps. Electrostatic induction laws apply in situations as far as the quasistatic approximation is valid. Electrostatic induction should not be confused with Electromagnetic induction, a normal uncharged piece of matter has equal numbers of positive and negative electric charges in each part of it, located close together, so no part of it has a net electric charge. The positive charges are the atoms nuclei which are bound into the structure of matter and are not free to move, the negative charges are the atoms electrons. In electrically conductive objects such as metals, some of the electrons are able to move freely about in the object. For example, if a charge is brought near the object. When the electrons out of an area, they leave an unbalanced positive charge due to the nuclei. This results in a region of negative charge on the object nearest to the charge. If the external charge is negative, the polarity of the regions will be reversed. Since this process is just a redistribution of the charges that were already in the object, it doesnt change the charge on the object. This induction effect is reversible, if the charge is removed. However, the effect can also be used to put a net charge on an object. When the contact with ground is broken, the object is left with a net negative charge and this method can be demonstrated using a gold-leaf electroscope, which is an instrument for detecting electric charge. The electroscope is first discharged, and an object is then brought close to the instruments top terminal. Since both leaves have the charge, they repel each other and spread apart
13.
Coulomb's law
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Coulombs law, or Coulombs inverse-square law, is a law of physics that describes force interacting between static electrically charged particles. The force of interaction between the charges is attractive if the charges have opposite signs and repulsive if like-signed, the law was first published in 1784 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism. It is analogous to Isaac Newtons inverse-square law of universal gravitation, Coulombs law can be used to derive Gausss law, and vice versa. The law has been tested extensively, and all observations have upheld the laws principle, ancient cultures around the Mediterranean knew that certain objects, such as rods of amber, could be rubbed with cats fur to attract light objects like feathers. Thales was incorrect in believing the attraction was due to a magnetic effect and he coined the New Latin word electricus to refer to the property of attracting small objects after being rubbed. This association gave rise to the English words electric and electricity, however, he did not generalize or elaborate on this. In 1767, he conjectured that the force between charges varied as the square of the distance. In 1769, Scottish physicist John Robison announced that, according to his measurements, in the early 1770s, the dependence of the force between charged bodies upon both distance and charge had already been discovered, but not published, by Henry Cavendish of England. Finally, in 1785, the French physicist Charles-Augustin de Coulomb published his first three reports of electricity and magnetism where he stated his law and this publication was essential to the development of the theory of electromagnetism. The torsion balance consists of a bar suspended from its middle by a thin fiber, the fiber acts as a very weak torsion spring. In Coulombs experiment, the balance was an insulating rod with a metal-coated ball attached to one end. The ball was charged with a charge of static electricity. The two charged balls repelled one another, twisting the fiber through an angle, which could be read from a scale on the instrument. By knowing how much force it took to twist the fiber through a given angle, the force is along the straight line joining them. If the two charges have the sign, the electrostatic force between them is repulsive, if they have different signs, the force between them is attractive. Coulombs law can also be stated as a mathematical expression. The vector form of the equation calculates the force F1 applied on q1 by q2, if r12 is used instead, then the effect on q2 can be found. It can be calculated using Newtons third law, F2 = −F1
14.
Gauss' law
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In physics, Gausss law, also known as Gausss flux theorem, is a law relating the distribution of electric charge to the resulting electric field. The law was first formulated by Joseph-Louis Lagrange in 1773, followed by Carl Friedrich Gauss in 1813 and it is one of Maxwells four equations, which form the basis of classical electrodynamics. Gausss law can be used to derive Coulombs law, and vice versa, in words, Gausss law states that, The net electric flux through any closed surface is equal to 1/ε times the net electric charge within that closed surface. Gausss law has a close similarity with a number of laws in other areas of physics, such as Gausss law for magnetism. The law can be expressed mathematically using vector calculus in integral form and differential form, Gausss law can be stated using either the electric field E or the electric displacement field D. Since the flux is defined as an integral of the electric field, however, much more often, it is the reverse problem that needs to be solved, The electric charge distribution is known, and the electric field needs to be computed. An exception is if there is symmetry in the situation. Then, if the flux is known, the field itself can be deduced at every point. Common examples of symmetries which lend themselves to Gausss law include cylindrical symmetry, planar symmetry, see the article Gaussian surface for examples where these symmetries are exploited to compute electric fields. The integral and differential forms are equivalent, by the divergence theorem. Here is the argument more specifically, in contrast, bound charge arises only in the context of dielectric materials. All these microscopic displacements add up to give a net charge distribution. Although microscopically, all charge is fundamentally the same, there are practical reasons for wanting to treat bound charge differently from free charge. The result is that the more fundamental Gausss law, in terms of E, is put into the equivalent form below, which is in terms of D. In homogeneous, isotropic, nondispersive, linear materials, there is a relationship between E and D, D = ε E where ε is the permittivity of the material. For the case of vacuum, ε = ε0, under these circumstances, Gausss law modifies to Φ E = Q f r e e ε for the integral form, and ∇ ⋅ E = ρ f r e e ε for the differential form. Gausss theorem can be interpreted in terms of the lines of force of the field as follows and this takes into account the direction of – field lines penetrating the surface considered with a minus sign in the opposite direction. Force lines begin or end only on charges, or may go to infinity
15.
Electric flux
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In electromagnetism, electric flux is the measure of flow of the electric field through a given area. It is typically represented by the Greek letter phi, Electric flux is proportional to the number of electric field lines going through a normally perpendicular surface. For a non-uniform electric field, the electric flux dΦE through a surface area dS is given by d Φ E = E ⋅ d S. This relation is known as Gauss law for electric field in its integral form, while Gauss Law holds for all situations, it is only useful for by hand calculations when high degrees of symmetry exist in the electric field. Examples include spherical and cylindrical symmetry, electrical flux has SI units of volt metres, or, equivalently, newton metres squared per coulomb. Thus, the SI base units of flux are kg·m3·s−3·A−1. Magnetic flux Maxwells equations Electric flux — HyperPhysics
16.
Electric potential energy
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An object may have electric potential energy by virtue of two key elements, its own electric charge and its relative position to other electrically charged objects. The SI unit of potential energy is the joule. In the CGS system the erg is the unit of energy, also electronvolts may be used,1 eV =1. 602×10−19 J. The following outline of proof states the derivation from the definition of electric potential energy, the electrostatic potential energy UE stored in a system of N charges q1, q2. A common question arises concerning the interaction of a point charge with its own electrostatic potential, since this interaction doesnt act to move the point charge itself, it doesnt contribute to the stored energy of the system. Consider bringing a point charge, q, into its position in the vicinity of a point charge. Some elements in a circuit can convert energy from one form to another, for example, a resistor converts electrical energy to heat. This is known as the Joule effect, a capacitor stores it in its electric field. These latter two expressions are only for cases when the smallest increment of charge is zero such as dielectrics in the presence of metallic electrodes or dielectrics containing many charges
17.
Electric dipole moment
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In physics, the electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the systems overall polarity. The electric field strength of the dipole is proportional to the magnitude of dipole moment, the SI units for electric dipole moment are Coulomb-meter, however the most commonly used unit is the Debye. Theoretically, a dipole is defined by the first-order term of the multipole expansion. This is unrealistic, as real dipoles have separated charge, however, because the charge separation is very small compared to everyday lengths, the error introduced by treating real dipoles like they are theoretically perfect is usually negligible. The direction of dipole is defined from the negative charge towards the positive charge. Often in physics the dimensions of an object can be ignored and can be treated as a pointlike object. Point particles with electric charge are referred to as point charges, two point charges, one with charge +q and the other one with charge −q separated by a distance d, constitute an electric dipole. For this case, the dipole moment has a magnitude p = q d and is directed from the negative charge to the positive one. Some authors may split d in half and use s = d/2 since this quantity is the distance between either charge and the centre of the dipole, leading to a factor of two in the definition. The electric dipole moment vector p also points from the charge to the positive charge. An idealization of this system is the electrical point dipole consisting of two charges only infinitesimally separated, but with a finite p. This quantity is used in the definition of polarization density, an object with an electric dipole moment is subject to a torque τ when placed in an external electric field. The torque tends to align the dipole with the field, a dipole aligned parallel to an electric field has lower potential energy than a dipole making some angle with it. For a spatially uniform electric field E, the torque is given by, τ = p × E, where p is the moment. The field vector and the dipole vector define a plane, a dipole orientes co- or anti-parallel to the direction in which a non-uniform electric field is increasing will not experience a torque, only a force in the direction of its dipole moment. It can be shown that this force will always be parallel to the dipole moment regardless of co- or anti-parallel orientation of the dipole. For an array of point charges, the density becomes a sum of Dirac delta functions, ρ = ∑ i =1 N q i δ. Substitution into the integration formula provides, p = ∑ i =1 N q i ∫ V δ d 3 r 0 = ∑ i =1 N q i
18.
Polarization density
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In classical electromagnetism, polarization density is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is placed in an electric field, its molecules gain electric dipole moment. The electric dipole moment induced per unit volume of the material is called the electric polarization of the dielectric. It can be compared to magnetization, which is the measure of the response of a material to a magnetic field in magnetism. The SI unit of measure is coulombs per square meter, an external electric field that is applied to a dielectric material, causes a displacement of bound charged elements. These are elements which are bound to molecules and are not free to move around the material, positive charged elements are displaced in the direction of the field, and negative charged elements are displaced opposite to the direction of the field. The molecules may remain neutral in charge, yet an electric dipole moment forms and this definition of polarization as a dipole moment per unit volume is widely adopted, though in some cases it can bring to ambiguities and paradoxes. Let a volume dV be isolated inside the dielectric, due to polarization the positive bound charge d q b + will be displaced a distance d relative to the negative bound charge d q b −, giving rise to a dipole moment d p = d q b d. Note that in this case χ simplifies to a scalar, although generally it is a tensor. This is a case due to the isotropy of the dielectric. And since free charges can get as close to the dielectric as to its topmost surface, it follows that polarization only gives rise to surface bound charge density. σ b may be related to P by the following equation, the class of dielectrics where the polarization density and the electric field are not in the same direction are known as anisotropic materials. The case of a dielectric medium is described by the field of crystal optics. The polarizability of individual particles in the medium can be related to the average susceptibility, in general, the susceptibility is a function of the frequency ω of the applied field. When the field is a function of time t, the polarization is a convolution of the Fourier transform of χ with the E. This reflects the fact that the dipoles in the material cannot respond instantaneously to the applied field, if the polarization P is not linearly proportional to the electric field E, the medium is termed nonlinear and is described by the field of nonlinear optics. In ferroelectric materials, there is no correspondence between P and E at all because of hysteresis. The behavior of electric fields, magnetic fields, charge density, in terms of volume charge densities, the free charge density ρ f is given by ρ f = ρ − ρ b where ρ is the total charge density
19.
Magnetostatics
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Magnetostatics is the study of magnetic fields in systems where the currents are steady. It is the analogue of electrostatics, where the charges are stationary. The magnetization need not be static, the equations of magnetostatics can be used to predict fast magnetic switching events that occur on scales of nanoseconds or less. Magnetostatics is even an approximation when the currents are not static — as long as the currents do not alternate rapidly. Magnetostatics is widely used in applications of such as models of magnetic recording devices. The fields are independent of time and each other, the magnetostatic equations, in both differential and integral forms, are shown in the table below. Where ∇ denotes divergence, and B is the flux density. Where J is the current density and H is the field intensity. The current going through the loop is I enc, the quality of this approximation may be guessed by comparing the above equations with the full version of Maxwells equations and considering the importance of the terms that have been removed. Of particular significance is the comparison of the J term against the ∂ D / ∂ t term, if the J term is substantially larger, then the smaller term may be ignored without significant loss of accuracy. A common technique is to solve a series of problems at incremental time steps. Plugging this result into Faradays Law finds a value for E and this method is not a true solution of Maxwells equations but can provide a good approximation for slowly changing fields. This includes air-core inductors and air-core transformers, one advantage of this technique is that, if a coil has a complex geometry, it can be divided into sections and the integral evaluated for each section. Since this equation is used to solve linear problems, the contributions can be added. For a very difficult geometry, numerical integration may be used, for problems where the dominant magnetic material is a highly permeable magnetic core with relatively small air gaps, a magnetic circuit approach is useful. When the air gaps are large in comparison to the circuit length, fringing becomes significant. The finite element calculation uses a form of the magnetostatic equations above in order to calculate magnetic potential. The value of B can be found from the magnetic potential, the magnetic field can be derived from the vector potential
20.
Magnetic field
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A magnetic field is the magnetic effect of electric currents and magnetic materials. The magnetic field at any point is specified by both a direction and a magnitude, as such it is represented by a vector field. The term is used for two distinct but closely related fields denoted by the symbols B and H, where H is measured in units of amperes per meter in the SI, B is measured in teslas and newtons per meter per ampere in the SI. B is most commonly defined in terms of the Lorentz force it exerts on moving electric charges, Magnetic fields can be produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. In quantum physics, the field is quantized and electromagnetic interactions result from the exchange of photons. Magnetic fields are used throughout modern technology, particularly in electrical engineering. The Earth produces its own field, which is important in navigation. Rotating magnetic fields are used in electric motors and generators. Magnetic forces give information about the carriers in a material through the Hall effect. The interaction of magnetic fields in electric devices such as transformers is studied in the discipline of magnetic circuits, noting that the resulting field lines crossed at two points he named those points poles in analogy to Earths poles. He also clearly articulated the principle that magnets always have both a north and south pole, no matter how finely one slices them, almost three centuries later, William Gilbert of Colchester replicated Petrus Peregrinus work and was the first to state explicitly that Earth is a magnet. Published in 1600, Gilberts work, De Magnete, helped to establish magnetism as a science, in 1750, John Michell stated that magnetic poles attract and repel in accordance with an inverse square law. Charles-Augustin de Coulomb experimentally verified this in 1785 and stated explicitly that the north and south poles cannot be separated, building on this force between poles, Siméon Denis Poisson created the first successful model of the magnetic field, which he presented in 1824. In this model, a magnetic H-field is produced by magnetic poles, three discoveries challenged this foundation of magnetism, though. First, in 1819, Hans Christian Ørsted discovered that an electric current generates a magnetic field encircling it, then in 1820, André-Marie Ampère showed that parallel wires having currents in the same direction attract one another. Finally, Jean-Baptiste Biot and Félix Savart discovered the Biot–Savart law in 1820, extending these experiments, Ampère published his own successful model of magnetism in 1825. This has the benefit of explaining why magnetic charge can not be isolated. Also in this work, Ampère introduced the term electrodynamics to describe the relationship between electricity and magnetism, in 1831, Michael Faraday discovered electromagnetic induction when he found that a changing magnetic field generates an encircling electric field
21.
Magnetization
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In classical electromagnetism, magnetization or magnetic polarization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Magnetization is not always uniform within a body, but rather varies between different points and it can be compared to electric polarization, which is the measure of the corresponding response of a material to an electric field in electrostatics. Physicists and engineers usually define magnetization as the quantity of magnetic moment per unit volume and it is represented by a pseudovector M. This is better illustrated through the following relation, m = ∭ M d V where m is a magnetic moment. Those definitions of P and M as a moments per unit volume are widely adopted, the M-field is measured in amperes per meter in SI units. The magnetization is often not listed as a parameter for commercially available ferromagnets. Instead the parameter that is listed is residual flux density, denoted B r, physicists often need the magnetization to calculate the moment of a ferromagnet. V is the volume of the magnet, μ0 =4 π ⋅10 −7 H/m is the permeability of vacuum. The behavior of magnetic fields, electric fields, charge density, the role of the magnetization is described below. The magnetization defines the magnetic field H as B = μ0 B = H +4 π M which is convenient for various calculations. The vacuum permeability μ0 is, by definition, 6993400000000000000♠4π×10−7 V·s/, a relation between M and H exists in many materials. In diamagnets and paramagnets, the relation is linear, M = χ m H where χm is called the volume magnetic susceptibility. In ferromagnets there is no correspondence between M and H because of Magnetic hysteresis. The magnetization M makes a contribution to the current density J and it is important to note that there is no such thing as a magnetic charge, but that issue was still debated through the whole 19th century. Other concepts, that went along with it, such as the auxiliary field H, however, they are convenient mathematical tools, and are therefore still used today for applications such as modeling the magnetic field of the Earth. The time-dependent behavior of magnetization becomes important when considering nanoscale and nanosecond timescale magnetization, technologically, this is one of the most important processes in magnetism that is linked to the magnetic data storage process such as used in modern hard disk drives. e. Incident electromagnetic radiation that is circularly polarized Demagnetization is the reduction or elimination of magnetization, another way is to pull it out of an electric coil with alternating current running through it, giving rise to fields that oppose the magnetization. One application of demagnetization is to eliminate unwanted magnetic fields, for example, magnetic fields can interfere with electronic devices such as cell phones or computers, and with machining by making cuttings cling to their parent
22.
Magnetic flux
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In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B passing through that surface. The SI unit of flux is the weber, and the CGS unit is the maxwell. Magnetic flux is measured with a fluxmeter, which contains measuring coils and electronics. The magnetic interaction is described in terms of a vector field, since a vector field is quite difficult to visualize at first, in elementary physics one may instead visualize this field with field lines. The magnetic flux through some surface, in this picture, is proportional to the number of field lines passing through that surface. In more advanced physics, the field line analogy is dropped, for a varying magnetic field, we first consider the magnetic flux through an infinitesimal area element dS, where we may consider the field to be constant, d Φ B = B ⋅ d S. This law is a consequence of the observation that magnetic monopoles have never been found. In other words, Gausss law for magnetism is the statement, while the magnetic flux through a closed surface is always zero, the magnetic flux through an open surface need not be zero and is an important quantity in electromagnetism. For example, a change in the flux passing through a loop of conductive wire will cause an electromotive force. The electromotive force is induced along this boundary, dℓ is an infinitesimal vector element of the contour ∂Σ, v is the velocity of the boundary ∂Σ, E is the electric field, B is the magnetic field. This equation is the principle behind an electrical generator, note that the flux of E through a closed surface is not always zero, this indicates the presence of electric monopoles, that is, free positive or negative charges. Gausss law gives the relation between the electric flux flowing out a surface and the electric charge enclosed in the surface. Magnetic circuit is a method using an analogy with electric circuits to calculate the flux of complex systems of magnetic components, Magnetic monopole is a hypothetical particle that may loosely be described as a magnet with only 1 pole. Magnetic flux quantum is the quantum of magnetic flux passing through a superconductor, carl Friedrich Gauss developed a fruitful collaboration with the physics professor Wilhelm Weber, it led to new knowledge in the field of magnetism. James Clerk Maxwell demonstrated that electric and magnetic forces are two aspects of electromagnetism. Patent 6,720,855, Magnetic-flux conduits Magnetic Flux through a Loop of Wire by Ernest Lee, conversion Magnetic flux Φ in nWb per meter track width to flux level in dB - Tape Operating Levels and Tape Alignment Levels
23.
Magnetic moment
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The magnetic moment of a magnet is a quantity that determines the torque it will experience in an external magnetic field. A loop of current, a bar magnet, an electron, a molecule. The magnetic moment may be considered to be a vector having a magnitude, the direction of the magnetic moment points from the south to north pole of the magnet. The magnetic field produced by the magnet is proportional to its magnetic moment, more precisely, the term magnetic moment normally refers to a systems magnetic dipole moment, which produces the first term in the multipole expansion of a general magnetic field. The dipole component of a magnetic field is symmetric about the direction of its magnetic dipole moment. The magnetic moment is defined as a vector relating the aligning torque on the object from an applied magnetic field to the field vector itself. The relationship is given by, τ = μ × B where τ is the acting on the dipole and B is the external magnetic field. This definition is based on how one would measure the magnetic moment, in principle, the unit for magnetic moment is not a base unit in the International System of Units. As the torque is measured in newton-meters and the field in teslas. This has equivalents in other units, N·m/T = A·m2 = J/T where A is amperes. In the CGS system, there are different sets of electromagnetism units, of which the main ones are ESU, Gaussian. The ratio of these two non-equivalent CGS units is equal to the speed of light in space, expressed in cm·s−1. All formulae in this article are correct in SI units, they may need to be changed for use in other unit systems. For example, in SI units, a loop of current with current I and area A has magnetic moment IA, the preferred classical explanation of a magnetic moment has changed over time. Before the 1930s, textbooks explained the moment using hypothetical magnetic point charges, since then, most have defined it in terms of Ampèrian currents. The sources of magnetic moments in materials can be represented by poles in analogy to electrostatics, consider a bar magnet which has magnetic poles of equal magnitude but opposite polarity. Each pole is the source of force which weakens with distance. Since magnetic poles always come in pairs, their forces partially cancel each other because while one pole pulls and this cancellation is greatest when the poles are close to each other i. e. when the bar magnet is short
24.
Gauss's law for magnetism
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In physics, Gausss law for magnetism is one of the four Maxwells equations that underlie classical electrodynamics. It states that the magnetic field B has divergence equal to zero, in other words and it is equivalent to the statement that magnetic monopoles do not exist. Rather than magnetic charges, the entity for magnetism is the magnetic dipole. Gausss law for magnetism can be written in two forms, a form and an integral form. These forms are equivalent due to the divergence theorem, the name Gausss law for magnetism is not universally used. The law is also called Absence of free magnetic poles, one reference even explicitly says the law has no name. It is also referred to as the transversality requirement because for plane waves it requires that the polarization be transverse to the direction of propagation, the differential form for Gausss law for magnetism is, where ∇ · denotes divergence, and B is the magnetic field. The left-hand side of equation is called the net flux of the magnetic field out of the surface. The integral and differential forms of Gausss law for magnetism are mathematically equivalent and that said, one or the other might be more convenient to use in a particular computation. The law in this states that for each volume element in space. No total magnetic charge can build up in any point in space, for example, the south pole of the magnet is exactly as strong as the north pole, and free-floating south poles without accompanying north poles are not allowed. In contrast, this is not true for other such as electric fields or gravitational fields. Due to the Helmholtz decomposition theorem, Gausss law for magnetism is equivalent to the following statement, the vector field A is called the magnetic vector potential. Note that there is more than one possible A which satisfies this equation for a given B field, for zero net magnetic charge density, the original form of Gausss magnetism law is the result. The modified formula in SI units is not standard, in one variation, magnetic charge has units of webers, where μ0 is the vacuum permeability. So far no magnetic monopoles have been found, despite extensive search and this idea, of the nonexistence of magnetic monopoles, originated in 1269 by Petrus Peregrinus de Maricourt. His work heavily influenced William Gilbert, whose 1600 work De Magnete spread the idea further, in the early 1800s Michael Faraday reintroduced this law, and it subsequently made it into James Clerk Maxwells electromagnetic field equations. Magnetic moment Vector calculus Integral Flux Gaussian surface Faradays law of induction Ampères circuital law Lorenz gauge condition
25.
Classical electromagnetism
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The theory provides an excellent description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible. For small distances and low field strengths, such interactions are described by quantum electrodynamics. Fundamental physical aspects of classical electrodynamics are presented in texts, such as those by Feynman, Leighton and Sands, Griffiths, Panofsky and Phillips. The physical phenomena that electromagnetism describes have been studied as separate fields since antiquity, for example, there were many advances in the field of optics centuries before light was understood to be an electromagnetic wave. For a detailed account, consult Pauli, Whittaker, Pais. The above equation illustrates that the Lorentz force is the sum of two vectors, one is the cross product of the velocity and magnetic field vectors. Based on the properties of the product, this produces a vector that is perpendicular to both the velocity and magnetic field vectors. The other vector is in the direction as the electric field. The sum of two vectors is the Lorentz force. In the absence of a field, the force is perpendicular to the velocity of the particle. If both electric and magnetic fields are present, the Lorentz force is the sum of both of these vectors, the electric field E is defined such that, on a stationary charge, F = q 0 E where q0 is what is known as a test charge. The size of the charge doesnt really matter, as long as it is small enough not to influence the field by its mere presence. What is plain from this definition, though, is that the unit of E is N/C and this unit is equal to V/m, see below. In electrostatics, where charges are not moving, around a distribution of point charges, both of the above equations are cumbersome, especially if one wants to determine E as a function of position. A scalar function called the potential can help. Electric potential, also called voltage, is defined by the line integral φ = − ∫ C E ⋅ d l where φ is the electric potential, unfortunately, this definition has a caveat. From Maxwells equations, it is clear that ∇ × E is not always zero, as a result, one must add a correction factor, which is generally done by subtracting the time derivative of the A vector potential described below. Whenever the charges are quasistatic, however, this condition will be essentially met, the scalar φ will add to other potentials as a scalar
26.
Lorentz force
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In physics the Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge q moving with velocity v in the presence of an electric field E, the first derivation of the Lorentz force is commonly attributed to Oliver Heaviside in 1889, although other historians suggest an earlier origin in an 1865 paper by James Clerk Maxwell. Hendrik Lorentz derived it a few years after Heaviside, the force F acting on a particle of electric charge q with instantaneous velocity v, due to an external electric field E and magnetic field B, is given by, where × is the vector cross product. More explicitly stated, F = q in which r is the vector of the charged particle, t is time. The term qE is called the force, while the term qv × B is called the magnetic force. According to some definitions, the term Lorentz force refers specifically to the formula for the magnetic force and this article will not follow this nomenclature, In what follows, the term Lorentz force will refer only to the expression for the total force. The magnetic force component of the Lorentz force manifests itself as the force acts on a current-carrying wire in a magnetic field. In that context, it is called the Laplace force. For a continuous distribution in motion, the Lorentz force equation becomes. If both sides of this equation are divided by the volume of this piece of the charge distribution dV. Rather than the amount of charge and its velocity in electric and magnetic fields, see Covariant formulation of classical electromagnetism for more details. The above-mentioned formulae use SI units which are the most common among experimentalists, technicians, in cgs-Gaussian units, which are somewhat more common among theoretical physicists, one has instead F = q c g s. where c is the speed of light. Where ε0 is the permittivity and μ0 the vacuum permeability. In practice, the subscripts cgs and SI are always omitted, early attempts to quantitatively describe the electromagnetic force were made in the mid-18th century. It was proposed that the force on magnetic poles, by Johann Tobias Mayer and others in 1760, however, in both cases the experimental proof was neither complete nor conclusive. It was not until 1784 when Charles-Augustin de Coulomb, using a balance, was able to definitively show through experiment that this was true. Soon after the discovery in 1820 by H. C, in all these descriptions, the force was always given in terms of the properties of the objects involved and the distances between them rather than in terms of electric and magnetic fields. J. J. Thomson was the first to attempt to derive from Maxwells field equations the electromagnetic forces on a charged object in terms of the objects properties
27.
Electromagnetic induction
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Electromagnetic or magnetic induction is the production of an electromotive force across an electrical conductor due to its dynamic interaction with a magnetic field. Michael Faraday is generally credited with the discovery of induction in 1831, Lenzs law describes the direction of the induced field. Faradays law was later generalized to become the Maxwell-Faraday equation, one of the four Maxwells equations in James Clerk Maxwells theory of electromagnetism, electromagnetic induction has found many applications in technology, including electrical components such as inductors and transformers, and devices such as electric motors and generators. Electromagnetic induction was first discovered by Michael Faraday, who made his discovery public in 1831 and it was discovered independently by Joseph Henry in 1832. In Faradays first experimental demonstration, he wrapped two wires around opposite sides of a ring or torus. He plugged one wire into a galvanometer, and watched it as he connected the wire to a battery. He saw a transient current, which he called a wave of electricity and this induction was due to the change in magnetic flux that occurred when the battery was connected and disconnected. Within two months, Faraday found several other manifestations of electromagnetic induction, Faraday explained electromagnetic induction using a concept he called lines of force. However, scientists at the time widely rejected his theoretical ideas, an exception was James Clerk Maxwell, who used Faradays ideas as the basis of his quantitative electromagnetic theory. Heavisides version is the form recognized today in the group of known as Maxwells equations. In 1834 Heinrich Lenz formulated the law named after him to describe the flux through the circuit, Lenzs law gives the direction of the induced EMF and current resulting from electromagnetic induction. Faradays law of induction makes use of the magnetic flux ΦB through a region of space enclosed by a wire loop. The magnetic flux is defined by an integral, Φ B = ∫ Σ B ⋅ d A. The dot product B·dA corresponds to an amount of magnetic flux. In more visual terms, the flux through the wire loop is proportional to the number of magnetic flux lines that pass through the loop. When the flux through the changes, Faradays law of induction says that the wire loop acquires an electromotive force. The direction of the force is given by Lenzs law which states that an induced current will flow in the direction that will oppose the change which produced it. This is due to the sign in the previous equation
28.
Faraday's law of induction
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It is the fundamental operating principle of transformers, inductors, and many types of electrical motors, generators and solenoids. The Maxwell–Faraday equation is a generalization of Faradays law, and is listed as one of Maxwells equations, electromagnetic induction was discovered independently by Michael Faraday in 1831 and Joseph Henry in 1832. Faraday was the first to publish the results of his experiments, in Faradays first experimental demonstration of electromagnetic induction, he wrapped two wires around opposite sides of an iron ring. He plugged one wire into a galvanometer, and watched it as he connected the wire to a battery. Indeed, he saw a transient current when he connected the wire to the battery and this induction was due to the change in magnetic flux that occurred when the battery was connected and disconnected. Within two months, Faraday had found several other manifestations of electromagnetic induction, Michael Faraday explained electromagnetic induction using a concept he called lines of force. However, scientists at the time widely rejected his theoretical ideas, an exception was James Clerk Maxwell, who used Faradays ideas as the basis of his quantitative electromagnetic theory. Heavisides version is the form recognized today in the group of known as Maxwells equations. Lenzs law, formulated by Heinrich Lenz in 1834, describes flux through the circuit, a different version, the Maxwell–Faraday equation, is valid in all circumstances. Faradays law of induction makes use of the magnetic flux ΦB through a hypothetical surface Σ whose boundary is a wire loop, since the wire loop may be moving, we write Σ for the surface. In more visual terms, the flux through the wire loop is proportional to the number of magnetic flux lines that pass through the loop. Equivalently, it is the voltage that would be measured by cutting the wire to create an open circuit, and attaching a voltmeter to the leads. Faradays law states that the EMF is also given by the rate of change of the flux, E = − d Φ B d t. The direction of the force is given by Lenzs law. The Maxwell–Faraday equation is where ∇ × is the operator and again E is the electric field. These fields can generally be functions of position r and time t, the Maxwell–Faraday equation is one of the four Maxwells equations, and therefore plays a fundamental role in the theory of classical electromagnetism. Dl is an infinitesimal element of the contour ∂Σ, dA is an infinitesimal vector element of surface Σ. If its direction is orthogonal to that surface patch, the magnitude is the area of a patch of surface
29.
Lenz's law
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Lenzs law is shown by the negative sign in Faradays law of induction, E = − ∂ Φ ∂ t, which indicates that the induced voltage and the change in magnetic flux have opposite signs. It is a law that specifies the direction of induced current. Lenzs law can be seen as analogous to Newtons third law in classic mechanics, for a rigorous mathematical treatment, see electromagnetic induction and Maxwells equations. If a change in the field of current i1 induces another electric current, i2. If these currents are in two coaxial circular conductors ℓ1 and ℓ2 respectively, and both are initially 0, then the currents i1 and i2 must counter-rotate, the opposing currents will repel each other as a result. Currents bound inside the atoms of strong magnets can create counter-rotating currents in a copper or aluminum pipe and this is shown by dropping the magnet through the pipe. The descent of the magnet inside the pipe is observably slower than when dropped outside the pipe, the induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant. In the examples below, if the flux is increasing, the field acts in opposition to it. If it is decreasing, the field acts in the direction of the applied field to oppose the change. In electromagnetism, when charges move along electric field lines work is done on them, when net positive work is applied to a charge q1, it gains speed and momentum. The net work on q1 thereby generates a field whose strength is proportional to the speed increase of q1. This magnetic field can interact with a neighboring charge q2, passing on this momentum to it, the charge q2 can also act on q1 in a similar manner, by which it returns some of the momentum that it received from q1. This back-and-forth component of momentum contributes to magnetic inductance, the closer that q1 and q2 are, the greater the effect. When q2 is inside a conductive medium such as a thick slab made of copper or aluminum, the energy of q1 is not instantly consumed as heat generated by the current of q2 but is also stored in two opposing magnetic fields. Momentum must be conserved in the process, so if q1 is pushed in one direction, however, the situation becomes more complicated when the finite speed of electromagnetic wave propagation is introduced. Famous 19th century electrodynamicist James Clerk Maxwell called this the electromagnetic momentum, yet, such a treatment of fields may be necessary when Lenzs law is applied to opposite charges. It is normally assumed that the charges in question have the same sign, if they do not, such as a proton and an electron, the interaction is different. An electron generating a field would generate an EMF that causes a proton to accelerate in the same direction as the electron
30.
Displacement current
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In electromagnetism, displacement current is a quantity appearing in Maxwells equations that is defined in terms of the rate of change of electric displacement field. Displacement current has the units as electric current, and it is a source of the magnetic field just as actual current is. However it is not a current of moving charges, but a time-varying electric field. In physical materials, there is also a contribution from the motion of charges bound in atoms. The idea was conceived by James Clerk Maxwell in his 1861 paper On Physical Lines of Force, Maxwell added displacement current to the electric current term in Ampères Circuital Law. In his 1865 paper A Dynamical Theory of the Electromagnetic Field Maxwell used this version of Ampères Circuital Law to derive the electromagnetic wave equation. This derivation is now accepted as a historical landmark in physics by virtue of uniting electricity, magnetism. The displacement current term is now seen as an addition that completed Maxwells equations and is necessary to explain many phenomena. The electric displacement field is defined as, D = ε0 E + P, the first term on the right hand side is present in material media and in free space. It doesnt necessarily come from any actual movement of charge, but it does have a magnetic field. Some authors apply the name displacement current to the first term by itself, the second term on the right hand side, called polarization current density, comes from the change in polarization of the individual molecules of the dielectric material. Polarization results when, under the influence of an electric field. The positive and negative charges in molecules separate, causing an increase in the state of polarization P, a changing state of polarization corresponds to charge movement and so is equivalent to a current, hence the term polarization current. Maxwell made no special treatment of the vacuum, treating it as a material medium, for Maxwell, the effect of P was simply to change the relative permittivity εr in the relation D = εrε0 E. The modern justification of displacement current is explained below, in this equation the use of ε accounts for the polarization of the dielectric. The scalar value of displacement current may also be expressed in terms of electric flux, the forms in terms of ε are correct only for linear isotropic materials. More generally ε may be replaced by a tensor, may depend upon the field itself. For a linear isotropic dielectric, the polarization P is given by, note that, ε = ε r ε0 = ε0
31.
Magnetic potential
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The term magnetic potential can be used for either of two quantities in classical electromagnetism, the magnetic vector potential, A, and the magnetic scalar potential, ψ. Both quantities can be used in circumstances to calculate the magnetic field. The more frequently used magnetic vector potential, A, is defined such that the curl of A is the magnetic field B, together with the electric potential, the magnetic vector potential can be used to specify the electric field, E as well. Therefore, many equations of electromagnetism can be either in terms of the E and B, or in terms of the magnetic vector potential. In more advanced such as quantum mechanics, most equations use the potentials. One important use of ψ is to determine the field due to permanent magnets when their magnetization is known. With some care the scalar potential can be extended to include free currents as well, historically, Lord Kelvin first introduced the concept of magnetic vector potential in 1851. He also showed the formula relating magnetic vector potential and magnetic field, in magnetostatics where there is no time-varying charge distribution, only the first equation is needed. Defining the electric and magnetic fields from potentials automatically satisfies two of Maxwells equations, Gausss law for magnetism and Faradays Law, for example, if A is continuous and well-defined everywhere, then it is guaranteed not to result in magnetic monopoles. Starting with the definitions, ∇ ⋅ B = ∇ ⋅ =0 ∇ × E = ∇ × = − ∂ ∂ t = − ∂ B ∂ t. Alternatively, the existence of A and ϕ is guaranteed from these two laws using the Helmholtzs theorem, for example, since the magnetic field is divergence-free, i. e. ∇ ⋅ B =0, A always exists that satisfies the above definition, the vector potential A is used when studying the Lagrangian in classical mechanics and in quantum mechanics. In the SI system, the units of A are V·s·m−1 and are the same as that of momentum per unit charge, although the magnetic field B is a pseudovector, the vector potential A is a polar vector. This is an example of a theorem, The curl of a polar vector is a pseudovector. Thus, there is a degree of freedom available when choosing A and this condition is known as gauge invariance. A different notation to write these same equations is shown below, the location r′ is a source point in the charge or current distribution. The earlier time t′ is called the time, and calculated as t ′ = t − | r − r ′ | c. There are a few things about A and ϕ calculated in this way
32.
Maxwell's equations
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Maxwells equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. They underpin all electric, optical and radio such as power generation, electric motors, wireless communication, cameras, televisions. Maxwells equations describe how electric and magnetic fields are generated by charges, currents, one important consequence of the equations is the demonstration of how fluctuating electric and magnetic fields can propagate at the speed of light. This electromagnetic radiation manifests itself in ways from radio waves to light. The equations have two major variants, the microscopic Maxwell equations have universal applicability but are unwieldy for common calculations. They relate the electric and magnetic fields to total charge and total current, including the complicated charges, the macroscopic Maxwell equations define two new auxiliary fields that describe the large-scale behaviour of matter without having to consider atomic scale details. However, their use requires experimentally determining parameters for a description of the electromagnetic response of materials. The term Maxwells equations is used for equivalent alternative formulations. The space-time formulations, are used in high energy and gravitational physics because they make the compatibility of the equations with special and general relativity manifest. In many situations, though, deviations from Maxwells equations are immeasurably small, exceptions include nonclassical light, photon-photon scattering, quantum optics, and many other phenomena related to photons or virtual photons. In the electric and magnetic field there are four equations. The two inhomogeneous equations describe how the fields vary in space due to sources, Gausss law describes how electric fields emanate from electric charges. Gausss law for magnetism describes magnetic fields as closed field lines not due to magnetic monopoles, the two homogeneous equations describe how the fields circulate around their respective sources. A separate law of nature, the Lorentz force law, describes how the electric and magnetic field act on charged particles, a version of this law was included in the original equations by Maxwell but, by convention, is no longer. The precise formulation of Maxwells equations depends on the definition of the quantities involved. Conventions differ with the systems, because various definitions and dimensions are changed by absorbing dimensionful factors like the speed of light c. This makes constants come out differently, the vector calculus formulation below has become standard. For formulations using tensor calculus or differential forms, see alternative formulations, for relativistically invariant formulations, see relativistic formulations
33.
Electromagnetic pulse
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An electromagnetic pulse, also sometimes called a transient electromagnetic disturbance, is a short burst of electromagnetic energy. Such a pulses origination may be a natural occurrence or man-made and can occur as a radiated, electric or magnetic field or an electric current. The management of EMP effects is an important branch of electromagnetic compatibility engineering, weapons have been developed to create the damaging effects of high-energy EMP. These are typically divided into nuclear and non-nuclear devices, such weapons, both real and fictional, have become known to the public by means of popular culture. An electromagnetic pulse is a short burst of electromagnetic energy and its short duration means that it will be spread over a range of frequencies. Pulses are typically characterized by, The type of energy, the range or spectrum of frequencies present. Pulse waveform, shape, duration and amplitude, the last two of these, the frequency spectrum and the pulse waveform, are interrelated via the Fourier transform and may be seen as two different ways of describing the same pulse. In general, only acts over long distances, with the others acting over short distances. There are a few exceptions, such as a solar magnetic flare, a pulse of electromagnetic energy typically comprises many frequencies from DC to some upper limit depending on the source. The range defined as EMP, sometimes referred to as DC to daylight, excludes the highest frequencies comprising the optical and ionizing ranges. Some types of EMP events can leave a trail, such as lightning and sparks. The waveform of a pulse describes how its instantaneous amplitude changes over time, real pulses tend to be quite complicated, so simplified models are often used. Such a model is shown either as a diagram or as a mathematical equation. Most pulses have a sharp leading edge, building up quickly to their maximum level. The classic model is a curve which climbs steeply, quickly reaches a peak. However, pulses from a switching circuit often approximate the form of a rectangular or square pulse. In a pulse train, such as from a digital clock circuit, EMP events usually induce a corresponding signal in the victim equipment, due to coupling between the source and victim. Coupling usually occurs most strongly over a narrow frequency band
34.
Electromagnetic radiation
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In physics, electromagnetic radiation refers to the waves of the electromagnetic field, propagating through space carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, light, ultraviolet, X-, classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric and magnetic fields that propagate at the speed of light through a vacuum. The oscillations of the two fields are perpendicular to other and perpendicular to the direction of energy and wave propagation. The wavefront of electromagnetic waves emitted from a point source is a sphere, the position of an electromagnetic wave within the electromagnetic spectrum can be characterized by either its frequency of oscillation or its wavelength. Electromagnetic waves are produced whenever charged particles are accelerated, and these waves can interact with other charged particles. EM waves carry energy, momentum and angular momentum away from their source particle, quanta of EM waves are called photons, whose rest mass is zero, but whose energy, or equivalent total mass, is not zero so they are still affected by gravity. Thus, EMR is sometimes referred to as the far field, in this language, the near field refers to EM fields near the charges and current that directly produced them, specifically, electromagnetic induction and electrostatic induction phenomena. In the quantum theory of electromagnetism, EMR consists of photons, quantum effects provide additional sources of EMR, such as the transition of electrons to lower energy levels in an atom and black-body radiation. The energy of a photon is quantized and is greater for photons of higher frequency. This relationship is given by Plancks equation E = hν, where E is the energy per photon, ν is the frequency of the photon, a single gamma ray photon, for example, might carry ~100,000 times the energy of a single photon of visible light. The effects of EMR upon chemical compounds and biological organisms depend both upon the power and its frequency. EMR of visible or lower frequencies is called non-ionizing radiation, because its photons do not individually have enough energy to ionize atoms or molecules, the effects of these radiations on chemical systems and living tissue are caused primarily by heating effects from the combined energy transfer of many photons. In contrast, high ultraviolet, X-rays and gamma rays are called ionizing radiation since individual photons of high frequency have enough energy to ionize molecules or break chemical bonds. These radiations have the ability to cause chemical reactions and damage living cells beyond that resulting from simple heating, Maxwell derived a wave form of the electric and magnetic equations, thus uncovering the wave-like nature of electric and magnetic fields and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the speed of light. Maxwell’s equations were confirmed by Heinrich Hertz through experiments with radio waves, according to Maxwells equations, a spatially varying electric field is always associated with a magnetic field that changes over time. Likewise, a varying magnetic field is associated with specific changes over time in the electric field. In an electromagnetic wave, the changes in the field are always accompanied by a wave in the magnetic field in one direction
35.
Maxwell stress tensor
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The Maxwell stress tensor is a second-order tensor used in classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum. In simple situations, such as a point charge moving freely in a magnetic field. When the situation more complicated, this ordinary procedure can become impossibly difficult. It is therefore convenient to many of these terms in the Maxwell stress tensor. Note that the above derivation assumes complete knowledge of both ρ and J, for the case of nonlinear materials, the nonlinear Maxwell stress tensor must be used. In physics, the Maxwell stress tensor is the tensor of an electromagnetic field. In Gaussian cgs unit, it is given by, σ i j =14 π, indeed, the diagonal elements give the tension acting on a differential area element normal to the corresponding axis. Unlike forces due to the pressure of a gas, an area element in the electromagnetic field also feels a force in a direction that is not normal to the element. This shear is given by the elements of the stress tensor. If the field is only magnetic, some of the drop out. It is the force which spins the motor. Br is the density in the radial direction, and Bt is the flux density in the tangential direction. John Wiley & Sons, Inc.1999, richard Becker, Electromagnetic Fields and Interactions, Dover Publications Inc.1964
36.
Poynting vector
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In physics, the Poynting vector represents the directional energy flux density of an electromagnetic field. The SI unit of the Poynting vector is the watt per square metre and it is named after its discoverer John Henry Poynting who first derived it in 1884. Oliver Heaviside and Nikolay Umov also independently discovered the Poynting vector and this expression is often called the Abraham form. The Poynting vector is denoted by S or N. In the microscopic version of Maxwells equations, this definition must be replaced by a definition in terms of the electric field E and the magnetic field B. It is also possible to combine the electric displacement field D with the magnetic field B to get the Minkowski form of the Poynting vector, or use D and H to construct yet another version. The choice has been controversial, Pfeifer et al. summarize, the Poynting vector represents the particular case of an energy flux vector for electromagnetic energy. However, any type of energy has its direction of movement in space, as well as its density, so energy flux vectors can be defined for types of energy as well. The Umov–Poynting vector discovered by Nikolay Umov in 1874 describes energy flux in liquid, in this definition, bound electrical currents are not included in this term, and instead contribute to S and u. For linear, nondispersive and isotropic materials, the relations can be written as D = ε E, H =1 μ B. Here ε and μ are scalar, real-valued constants independent of position, direction, in principle, this limits Poyntings theorem in this form to fields in vacuum and nondispersive linear materials. A generalization to dispersive materials is possible under certain circumstances at the cost of additional terms, the microscopic version of Maxwells equations admits only the fundamental fields E and B, without a built-in model of material media. Only the vacuum permittivity and permeability are used, and there is no D or H. When this model is used, the Poynting vector is defined as S =1 μ0 E × B and it can be derived directly from Maxwells equations in terms of total charge and current and the Lorentz force law only. The two alternative definitions of the Poynting vector are equal in vacuum or in non-magnetic materials, where B = μ0H and this is especially true for the electromagnetic energy density, in contrast to the macroscopic form E × H. The above form for the Poynting vector represents the power flow due to instantaneous electric and magnetic fields. More commonly, problems in electromagnetics are solved in terms of sinusoidally varying fields at a specified frequency, the results can then be applied more generally, for instance, by representing incoherent radiation as a superposition of such waves at different frequencies and with fluctuating amplitudes. We would thus not be considering the instantaneous E and H used above, note that these complex amplitude vectors are not functions of time, as they are understood to refer to oscillations over all time
37.
Jefimenko's equations
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In electromagnetism, Jefimenkos equations describe the behavior of the electric and magnetic fields in terms of the charge and current distributions at retarded times. There are similar expressions for D and H. However, Jefimenkos equations show an alternative point of view, Jefimenko says. neither Maxwells equations nor their solutions indicate an existence of causal links between electric and magnetic fields. As pointed out by McDonald, Jefimenkos equations seem to appear first in 1962 in the edition of Panofsky. Essential features of these equations are easily observed which is that the right hand sides involve retarded time which reflects the causality of the expressions. In other words, the side of each equation is actually caused by the right side. In the typical expressions for Maxwells equations there is no doubt that both sides are equal to other, but as Jefimenko notes. Since each of these equations connects quantities simultaneous in time, none of these equations can represent a causal relation, the second feature is that the expression for E does not depend upon B and vice versa. Hence, it is impossible for E and B fields to be creating each other, charge density and current density are creating them both
38.
Eddy current
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Eddy currents are loops of electrical current induced within conductors by a changing magnetic field in the conductor, due to Faradays law of induction. Eddy currents flow in closed loops within conductors, in perpendicular to the magnetic field. By Lenzs law, an eddy current creates a field that opposes the magnetic field that created it. For example, a conductive surface will exert a drag force on a moving magnet that opposes its motion. This effect is employed in eddy current brakes which are used to stop rotating power tools quickly when they are turned off, the current flowing through the resistance of the conductor also dissipates energy as heat in the material. Eddy currents are used to heat objects in induction heating furnaces and equipment. The term eddy current comes from analogous currents seen in water in fluid dynamics, somewhat analogously, eddy currents can take time to build up and can persist for very short times in conductors due to their inductance. The first person to observe eddy currents was François Arago, the 25th Prime Minister of France, in 1824 he observed what has been called rotatory magnetism, and that most conductive bodies could be magnetized, these discoveries were completed and explained by Michael Faraday. Eddy currents produce a field that cancels a part of the external field. French physicist Léon Foucault is credited with having discovered eddy currents, the first use of eddy current for non-destructive testing occurred in 1879 when David E. Hughes used the principles to conduct metallurgical sorting tests. A magnet induces circular electric currents in a metal sheet moving past it and it shows a metal sheet moving to the right under a stationary magnet. The magnetic field of the north pole N passes down through the sheet. Since the metal is moving, the flux through the sheet is changing. At the part of the sheet under the edge of the magnet the magnetic field through the sheet is increasing as it gets nearer the magnet. From Faradays law of induction, this creates an electric field in the sheet in a counterclockwise direction around the magnetic field lines. This field induces a flow of electric current, in the sheet. At the trailing edge of the magnet the magnetic field through the sheet is decreasing, d B d t <0, the mobile charge carriers in the metal, the electrons, actually have a negative charge so their motion is opposite in direction to the conventional current shown. Both of these forces oppose the motion of the sheet, the kinetic energy which is consumed overcoming this drag force is dissipated as heat by the currents flowing through the resistance of the metal, so the metal gets warm under the magnet
39.
London equations
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The London equations, developed by brothers Fritz and Heinz London in 1935, relate current to electromagnetic fields in and around a superconductor. Arguably the simplest meaningful description of superconducting phenomena, they form the genesis of almost any modern introductory text on the subject. A major triumph of the equations is their ability to explain the Meissner effect, wherein a material exponentially expels all internal magnetic fields as it crosses the superconducting threshold. There are two London equations when expressed in terms of fields, ∂ j s ∂ t = n s e 2 m E, ∇ × j s = − n s e 2 m B. Throughout this article SI units are employed, the last equation suffers from only the disadvantage that it is not gauge invariant, but is true only in the Coulomb gauge, where the divergence of A is zero. This equation holds for magnetic fields that vary slowly in space, thus, the London equations imply a characteristic length scale, λ, over which external magnetic fields are exponentially suppressed. This value is the London penetration depth, if x leads perpendicular to the boundary then the solution inside the superconductor may be shown to be B z = B0 e − x / λ. From here the meaning of the London penetration depth can perhaps most easily be discerned. While it is important to note that the equations cannot be formally derived. Substances across a wide range of composition behave roughly according to Ohms law. However, such a relationship is impossible in a superconductor for, almost by definition. To this end, the London brothers imagined electrons as if they were free electrons under the influence of an external electric field. According to the Lorentz force law F = e E + e v × B these electrons should encounter a uniform force and this is precisely what the first London equation states. To obtain the equation, take the curl of the first London equation and apply Faradays law, ∇ × E = − ∂ B ∂ t. As it currently stands, this equation permits both constant and exponentially decaying solutions and this results in the second London equation. It is also possible to justify the London equations by other means, the velocity operator v =1 m is defined by dividing the gauge-invariant, kinematic momentum operator by the particle mass m. We may then make this replacement in the equation above and this leaves j s = − n s e s 2 m A, which is the London equation according to the second formulation above
40.
Electrical network
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An electrical network is an interconnection of electrical components or a model of such an interconnection, consisting of electrical elements. An electrical circuit is a network consisting of a closed loop, linear electrical networks, a special type consisting only of sources, linear lumped elements, and linear distributed elements, have the property that signals are linearly superimposable. They are thus more easily analyzed, using powerful frequency domain methods such as Laplace transforms, to determine DC response, AC response, a resistive circuit is a circuit containing only resistors and ideal current and voltage sources. Analysis of resistive circuits is less complicated than analysis of circuits containing capacitors and inductors, if the sources are constant sources, the result is a DC circuit. A network that contains active components is known as an electronic circuit. Such networks are generally nonlinear and require more complex design and analysis tools, an active network is a network that contains an active source – either a voltage source or current source. A passive network is a network that does not contain an active source, a network is linear if its signals obey the principle of superposition, otherwise it is non-linear. Sources can be classified as independent sources and dependent sources Ideal Independent Source maintains same voltage or current regardless of the elements present in the circuit. Its value is either constant or sinusoidal, the strength of voltage or current is not changed by any variation in connected network. Dependent Sources depend upon a particular element of the circuit for delivering the power or voltage or current depending upon the type of source it is, a number of electrical laws apply to all electrical networks. These include, Kirchhoffs current law, The sum of all currents entering a node is equal to the sum of all currents leaving the node, Kirchhoffs voltage law, The directed sum of the electrical potential differences around a loop must be zero. Ohms law, The voltage across a resistor is equal to the product of the resistance, nortons theorem, Any network of voltage or current sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor. Thévenins theorem, Any network of voltage or current sources and resistors is electrically equivalent to a voltage source in series with a single resistor. Other more complex laws may be needed if the network contains nonlinear or reactive components, non-linear self-regenerative heterodyning systems can be approximated. Applying these laws results in a set of equations that can be solved either algebraically or numerically. To design any electrical circuit, either analog or digital, electrical engineers need to be able to predict the voltages, simple linear circuits can be analyzed by hand using complex number theory. In more complex cases the circuit may be analyzed with specialized programs or estimation techniques such as the piecewise-linear model. More complex circuits can be analyzed numerically with software such as SPICE or GNUCAP, once the steady state solution is found, the operating points of each element in the circuit are known
41.
Electric current
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An electric current is a flow of electric charge. In electric circuits this charge is carried by moving electrons in a wire. It can also be carried by ions in an electrolyte, or by both ions and electrons such as in an ionised gas. The SI unit for measuring a current is the ampere. Electric current is measured using a device called an ammeter, electric currents cause Joule heating, which creates light in incandescent light bulbs. They also create magnetic fields, which are used in motors, inductors and generators, the particles that carry the charge in an electric current are called charge carriers. In metals, one or more electrons from each atom are loosely bound to the atom and these conduction electrons are the charge carriers in metal conductors. The conventional symbol for current is I, which originates from the French phrase intensité de courant, current intensity is often referred to simply as current. The I symbol was used by André-Marie Ampère, after whom the unit of current is named, in formulating the eponymous Ampères force law. The notation travelled from France to Great Britain, where it became standard, in a conductive material, the moving charged particles which constitute the electric current are called charge carriers. In other materials, notably the semiconductors, the carriers can be positive or negative. Positive and negative charge carriers may even be present at the same time, a flow of positive charges gives the same electric current, and has the same effect in a circuit, as an equal flow of negative charges in the opposite direction. Since current can be the flow of positive or negative charges. The direction of current is arbitrarily defined as the same direction as positive charges flow. This is called the direction of current I. If the current flows in the direction, the variable I has a negative value. When analyzing electrical circuits, the direction of current through a specific circuit element is usually unknown. Consequently, the directions of currents are often assigned arbitrarily
42.
Electric potential
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An electric potential is the amount of work needed to move a unit positive charge from a reference point to a specific point inside the field without producing any acceleration. Typically, the point is Earth or a point at Infinity. By dividing out the charge on the particle a remainder is obtained that is a property of the field itself. This value can be calculated in either a static or an electric field at a specific time in units of joules per coulomb. The electric potential at infinity is assumed to be zero, a generalized electric scalar potential is also used in electrodynamics when time-varying electromagnetic fields are present, but this can not be so simply calculated. The electric potential and the vector potential together form a four vector. Classical mechanics explores concepts such as force, energy, potential etc, force and potential energy are directly related. A net force acting on any object will cause it to accelerate, as it rolls downhill its potential energy decreases, being translated to motion, inertial energy. It is possible to define the potential of certain force fields so that the energy of an object in that field depends only on the position of the object with respect to the field. Two such force fields are the field and an electric field. Such fields must affect objects due to the properties of the object. Objects may possess a property known as charge and an electric field exerts a force on charged objects. If the charged object has a charge the force will be in the direction of the electric field vector at that point while if the charge is negative the force will be in the opposite direction. The magnitude of the force is given by the quantity of the charge multiplied by the magnitude of the field vector. The electric potential at a point r in an electric field E is given by the line integral where C is an arbitrary path connecting the point with zero potential to r. When the curl ∇ × E is zero, the integral above does not depend on the specific path C chosen. The concept of electric potential is linked with potential energy. A test charge q has a potential energy UE given by U E = q V
43.
Voltage
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Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential energy between two points per unit electric charge. The voltage between two points is equal to the work done per unit of charge against an electric field to move the test charge between two points. This is measured in units of volts, voltage can be caused by static electric fields, by electric current through a magnetic field, by time-varying magnetic fields, or some combination of these three. A voltmeter can be used to measure the voltage between two points in a system, often a reference potential such as the ground of the system is used as one of the points. A voltage may represent either a source of energy or lost, used, given two points in space, x A and x B, voltage is the difference in electric potential between those two points. Electric potential must be distinguished from electric energy by noting that the potential is a per-unit-charge quantity. Like mechanical potential energy, the zero of electric potential can be chosen at any point, so the difference in potential, i. e. the voltage, is the quantity which is physically meaningful. The voltage between point A to point B is equal to the work which would have to be done, per unit charge, against or by the electric field to move the charge from A to B. The voltage between the two ends of a path is the energy required to move a small electric charge along that path. Mathematically this is expressed as the integral of the electric field. In the general case, both an electric field and a dynamic electromagnetic field must be included in determining the voltage between two points. Historically this quantity has also called tension and pressure. Pressure is now obsolete but tension is used, for example within the phrase high tension which is commonly used in thermionic valve based electronics. Voltage is defined so that negatively charged objects are pulled towards higher voltages, therefore, the conventional current in a wire or resistor always flows from higher voltage to lower voltage. Current can flow from lower voltage to higher voltage, but only when a source of energy is present to push it against the electric field. This is the case within any electric power source, for example, inside a battery, chemical reactions provide the energy needed for ion current to flow from the negative to the positive terminal. The electric field is not the only factor determining charge flow in a material, the electric potential of a material is not even a well defined quantity, since it varies on the subatomic scale. A more convenient definition of voltage can be found instead in the concept of Fermi level, in this case the voltage between two bodies is the thermodynamic work required to move a unit of charge between them
44.
Ohm's law
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Ohms law states that the current through a conductor between two points is directly proportional to the voltage across the two points. More specifically, Ohms law states that the R in this relation is constant, independent of the current and he presented a slightly more complex equation than the one above to explain his experimental results. The above equation is the form of Ohms law. In physics, the term Ohms law is used to refer to various generalizations of the law originally formulated by Ohm. This reformulation of Ohms law is due to Gustav Kirchhoff, in January 1781, before Georg Ohms work, Henry Cavendish experimented with Leyden jars and glass tubes of varying diameter and length filled with salt solution. He measured the current by noting how strong a shock he felt as he completed the circuit with his body, Cavendish wrote that the velocity varied directly as the degree of electrification. He did not communicate his results to other scientists at the time, francis Ronalds delineated “intensity” and “quantity” for the dry pile – a high voltage source – in 1814 using a gold-leaf electrometer. He found for a dry pile that the relationship between the two parameters was not proportional under certain meteorological conditions, Ohm did his work on resistance in the years 1825 and 1826, and published his results in 1827 as the book Die galvanische Kette, mathematisch bearbeitet. He drew considerable inspiration from Fouriers work on heat conduction in the explanation of his work. For experiments, he initially used voltaic piles, but later used a thermocouple as this provided a stable voltage source in terms of internal resistance. He used a galvanometer to measure current, and knew that the voltage between the terminals was proportional to the junction temperature. He then added test wires of varying length, diameter, from this, Ohm determined his law of proportionality and published his results. Ohms law was probably the most important of the early descriptions of the physics of electricity. We consider it almost obvious today, when Ohm first published his work, this was not the case, critics reacted to his treatment of the subject with hostility. They called his work a web of naked fancies and the German Minister of Education proclaimed that a professor who preached such heresies was unworthy to teach science, also, Ohms brother Martin, a mathematician, was battling the German educational system. These factors hindered the acceptance of Ohms work, and his work did not become widely accepted until the 1840s, fortunately, Ohm received recognition for his contributions to science well before he died. While the old term for electrical conductance, the mho, is used, a new name. The siemens is preferred in formal papers, Ohms work long preceded Maxwells equations and any understanding of frequency-dependent effects in AC circuits
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