1.
Lorentz force
–
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
Lorentz force
–
Beam of electrons moving in a circle, due to the presence of a magnetic field. Purple light is emitted along the electron path, due to the electrons colliding with gas molecules in the bulb. A
Teltron tube is used in this example.
Lorentz force
–
Lorentz force F on a
charged particle (of charge q) in motion (instantaneous velocity v). The
E field and
B field vary in space and time.
2.
Electromagnet
–
An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. The magnetic field disappears when the current is turned off, electromagnets usually consist of insulated wire wound into a coil. A current through the wire creates a field which is concentrated in the hole in the center of the coil. The main advantage of an electromagnet over a permanent magnet is that the field can be quickly changed by controlling the amount of electric current in the winding. However, unlike a permanent magnet that needs no power, an electromagnet requires a supply of current to maintain the magnetic field. Electromagnets are also employed in industry for picking up and moving heavy objects such as scrap iron. Danish scientist Hans Christian Ørsted discovered in 1820 that electric currents create magnetic fields, british scientist William Sturgeon invented the electromagnet in 1824. His first electromagnet was a piece of iron that was wrapped with about 18 turns of bare copper wire. The iron was varnished to insulate it from the windings, when a current was passed through the coil, the iron became magnetized and attracted other pieces of iron, when the current was stopped, it lost magnetization. Sturgeon displayed its power by showing that although it only weighed seven ounces, however, Sturgeons magnets were weak because the uninsulated wire he used could only be wrapped in a single spaced out layer around the core, limiting the number of turns. Beginning in 1830, US scientist Joseph Henry systematically improved and popularized the electromagnet, the first major use for electromagnets was in telegraph sounders. A portative electromagnet is one designed to just hold material in place, a tractive electromagnet applies a force and moves something. The solenoid is a coil of wire, and the plunger is made of a such as soft iron. Applying a current to the solenoid applies a force to the plunger, the plunger stops moving when the forces upon it are balanced. For example, the forces are balanced when the plunger is centered in the solenoid, the maximum uniform pull happens when one end of the plunger is at the middle of the solenoid. For units using inches, pounds force, and amperes with long, slender, solenoids, for example, a 12-inch long coil with a long plunger of 1-square inch cross section and 11,200 ampere-turns had a maximum pull of 8.75 pounds. The maximum pull is increased when a stop is inserted into the solenoid. The stop becomes a magnet that will attract the plunger, it adds little to the pull when the plunger is far away
Electromagnet
–
Industrial electromagnet lifting scrap iron, 1914
Electromagnet
–
A simple electromagnet consisting of a coil of insulated wire wrapped around an iron core. A core of ferromagnetic material like iron serves to increase the magnetic field created. The strength of magnetic field generated is proportional to the amount of current through the winding.
Electromagnet
–
Laboratory electromagnet. Produces 2 T field with 20 A current.
Electromagnet
–
Magnet in a
mass spectrometer
3.
Electricity
–
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
Electricity
–
Lightning is one of the most dramatic effects of electricity.
Electricity
–
Thales, the earliest known researcher into electricity
Electricity
–
Benjamin Franklin conducted extensive research on electricity in the 18th century, as documented by
Joseph Priestley (1767) History and Present Status of Electricity, with whom Franklin carried on extended correspondence.
Electricity
–
Michael Faraday 's discoveries formed the foundation of electric motor technology
4.
Magnetism
–
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
Magnetism
–
Drawing of a medical treatment using magnetic brushes.
Charles Jacque 1843, France.
Magnetism
–
A magnetic quadrupole
Magnetism
–
Michael Faraday, 1842
Magnetism
–
A permanent magnet holding up several coins
5.
Electrostatics
–
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
Electrostatics
–
Paper strips attracted by a charged CD
Electrostatics
–
Lightning over
Oradea in
Romania
6.
Electric charge
–
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
Electric charge
–
Electric field of a positive and a negative point charge.
7.
Static electricity
–
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
Static electricity
–
Contact with the slide has left this child's hair positively charged so that the individual hairs repel one another. The hair can also be attracted to the negatively charged slide surface.
Static electricity
–
A
network card inside an
antistatic bag.
Static electricity
–
An
antistatic wrist strap with
crocodile clip.
Static electricity
–
Natural static discharge
8.
Electric field
–
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
Electric field
–
Electric field lines emanating from a point positive
electric charge suspended over an infinite sheet of conducting material.
9.
Electrical conductor
–
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
Electrical conductor
–
Overhead conductors carry electric power from generating stations to customers.
10.
Insulator (electricity)
–
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
Insulator (electricity)
–
Ceramic insulator used on railways electrified with 25kV AC overhead electrical catenary
Insulator (electricity)
–
Conducting
copper wire insulated by an outer layer of
polyethylene
Insulator (electricity)
–
3-core copper wire power cable, each core with individual colour-coded insulating sheaths all contained within an outer protective sheath
Insulator (electricity)
–
PVC-sheathed
Mineral insulated copper cable with 2 conducting cores
11.
Triboelectric effect
–
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
Triboelectric effect
–
Electromagnetism
12.
Electrostatic discharge
–
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
Electrostatic discharge
–
A portion of a
static discharger on an aircraft. Note the two sharp 3/8" metal micropoints and the protective yellow plastic.
Electrostatic discharge
–
Lightning over Rymań. Northern
Poland.
Electrostatic discharge
–
A
network card inside an
antistatic bag, a bag made of a partially conductive plastic that acts as a
Faraday cage, shielding the card from ESD.
Electrostatic discharge
–
Electric discharge showing the ribbon-like
plasma filaments from multiple discharges from a
Tesla coil.
13.
Electrostatic induction
–
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
Electrostatic induction
Electrostatic induction
–
Demonstration of induction, in the 1870s. The positive terminal of an
electrostatic machine is placed near an uncharged brass cylinder, causing the left end to acquire a positive charge and the right to acquire a negative charge. The small
pith ball electroscopes hanging from the bottom show that the charge is concentrated at the ends.
14.
Electric flux
–
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
Electric flux
–
Electromagnetism
15.
Electric potential energy
–
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
Electric potential energy
–
The electric potential energy stored in a
capacitor is U E =½ CV 2
Electric potential energy
–
Electrostatic potential energy of q due to Q 1 and Q 2 charge system:
16.
Electric dipole moment
–
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
Electric dipole moment
–
An electric dipole potential map. In blue negative potentials while in red positive ones.
Electric dipole moment
–
Electromagnetism
Electric dipole moment
–
A uniform array of identical dipoles is equivalent to a surface charge.
Electric dipole moment
17.
Polarization density
–
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
Polarization density
–
Above: an elementary volume d V = d V 1 + d V 2 (bounded by the element of area d A) so small, that the dipole enclosed by it can be thought as that produce by two elementary opposite charges. Below, a planar view (click in the image to enlarge).
Polarization density
–
Electromagnetism
Polarization density
18.
Magnetostatics
–
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
Magnetostatics
–
Electromagnetism
19.
Magnetic field
–
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
Magnetic field
–
One of the first drawings of a magnetic field, by
René Descartes, 1644. It illustrated his theory that magnetism was caused by the circulation of tiny helical particles, "threaded parts", through threaded pores in magnets.
Magnetic field
–
Magnetic field of an ideal cylindrical
magnet with its axis of symmetry inside the image plane. The magnetic field is represented by
magnetic field lines, which show the direction of the field at different points.
Magnetic field
–
Hans Christian Ørsted, Der Geist in der Natur, 1854
20.
Magnetization
–
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
Magnetization
–
Electromagnetism
21.
Magnetic flux
–
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
Magnetic flux
–
Area defined by an electric coil with three turns.
Magnetic flux
–
The magnetic flux through a surface when the magnetic field is variable relies on splitting the surface into small surface elements, over which the magnetic field can be considered to be locally constant. The total flux is then a formal summation of these surface elements (see
surface integration).
22.
Magnetic moment
–
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
Magnetic moment
–
Magnetic field lines around a "magnetostatic dipole". The magnetic dipole itself is located in the center of the figure, seen from the side, and pointing upward.
Magnetic moment
–
An electrostatic analog for a magnetic moment: two opposing charges separated by a finite distance.
23.
Classical electromagnetism
–
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
Classical electromagnetism
–
Electromagnetism
24.
Electromagnetic induction
–
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
Electromagnetic induction
–
Faraday's disk (see
homopolar generator)
Electromagnetic induction
Electromagnetic induction
Electromagnetic induction
25.
Displacement current
–
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
Displacement current
–
An electrically charging capacitor with an imaginary cylindrical surface surrounding the left-hand plate. Right-hand surface R lies in the space between the plates and left-hand surface L lies to the left of the left plate. No conduction current enters cylinder surface R, while current I leaves through surface L. Consistency of Ampère's law requires a displacement current I D = I to flow across surface R.
Displacement current
–
Example showing two surfaces S 1 and S 2 that share the same bounding contour ∂S. However, S 1 is pierced by conduction current, while S 2 is pierced by displacement current.
26.
Magnetic potential
–
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
Magnetic potential
–
Electromagnetism
27.
Electromagnetic field
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An electromagnetic field is a physical field produced by electrically charged objects. It affects the behavior of charged objects in the vicinity of the field, the electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction. It is one of the four forces of nature. The field can be viewed as the combination of an electric field, the electric field is produced by stationary charges, and the magnetic field by moving charges, these two are often described as the sources of the field. The way in which charges and currents interact with the field is described by Maxwells equations. The electromagnetic field may be viewed in two ways, a continuous structure or a discrete structure. Classically, electric and magnetic fields are thought of as being produced by smooth motions of charged objects, for example, oscillating charges produce electric and magnetic fields that may be viewed in a smooth, continuous, wavelike fashion. In this case, energy is viewed as being transferred continuously through the field between any two locations. For instance, the atoms in a radio transmitter appear to transfer energy continuously. This view is useful to an extent, but problems are found at high frequencies. The electromagnetic field may be thought of in a more coarse way, experiments reveal that in some circumstances electromagnetic energy transfer is better described as being carried in the form of packets called quanta with a fixed frequency. Plancks relation links the photon energy E of a photon to its frequency ν through the equation, E = h ν where h is Plancks constant, and ν is the frequency of the photon. It is found that increasing the intensity of the incident radiation increases only the number of electrons ejected, only the frequency of the radiation is relevant to the energy of the ejected electrons. It also gives rise to quantum optics, which is different from quantum electrodynamics in that the matter itself is modelled using quantum mechanics rather than quantum field theory. In the past, electrically charged objects were thought to produce two different, unrelated types of field associated with their charge property, over time, it was realized that the electric and magnetic fields are better thought of as two parts of a greater whole — the electromagnetic field. Until 1820, when the Danish physicist H. C, Ørsted discovered the effect of electricity through a wire on a compass needle, electricity and magnetism had been viewed as unrelated phenomena. If these other charges and currents are comparable in size to the producing the above electromagnetic field. Thus, the field may be viewed as a dynamic entity that causes other charges and currents to move
Electromagnetic field
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Electromagnetism
28.
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
Electromagnetic pulse
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EMP simulator HAGII-C testing a
Boeing E-4 aircraft.
Electromagnetic pulse
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Rectangular pulse
Electromagnetic pulse
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EMPRESS I (antennae along shoreline) with
USS Estocin (FFG-15) moored in the foreground for testing.
29.
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
Electromagnetic radiation
30.
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
Maxwell stress tensor
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Lorentz force (per unit 3-volume) f on a continuous
charge distribution (
charge density ρ) in motion. The 3-
current density J corresponds to the motion of the charge element dq in
volume element dV and varies throughout the continuum.