Electrostatics
Electrostatics is a branch of physics that studies electric charges at rest. Since classical physics, it has been 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; such forces are described by Coulomb's law. Though electrostatically induced forces seem to be rather weak, some electrostatic forces such as the one between an electron and a proton, that together make up a hydrogen atom, is about 36 orders of magnitude stronger than the gravitational force acting between them. There are many examples of electrostatic phenomena, from those as simple as the attraction of the plastic wrap to one's hand after it is removed from a package to the spontaneous explosion of grain silos, the damage of electronic components during manufacturing, photocopier & laser printer operation. Electrostatics involves the buildup of charge on the surface of objects due to contact with other surfaces.
Although charge exchange happens whenever any two surfaces contact and separate, the effects of charge exchange are only noticed when at least one of the surfaces has a high resistance to electrical flow. This is because the charges that transfer are trapped there for a time long enough for their effects to be observed; these charges remain on the object until they either bleed off to ground or are neutralized by a discharge: e.g. the familiar phenomenon of a static'shock' is caused by the neutralization of charge built up in the body from contact with insulated surfaces. Coulomb's law states that:'The magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them.' The force is along the straight line joining them. If the two charges have the same sign, the electrostatic force between them is repulsive. If r is the distance between two charges the force between two point charges q and Q is: F = 1 4 π ε 0 q Q r 2 = k 0 q Q r 2, where ε0 is the vacuum permittivity, or permittivity of free space: ε 0 ≈ 10 − 9 36 π C 2 N − 1 m − 2 ≈ 8.854 187 817 × 10 − 12 C 2 N − 1 m − 2.
The SI units of ε0 are equivalently A2s4 kg−1m−3 or C2N−1m−2 or F m−1. Coulomb's constant is: k 0 = 1 4 π ε 0 ≈ 8.987 551 787 × 10 9 N m 2 C − 2. A single proton has a charge of e, the electron has a charge of −e, where, e ≈ 1.602 176 565 × 10 − 19 C. These physical constants are defined so that ε0 and k0 are defined, e is a measured quantity; the electric field, E →, in units of newtons per coulomb or volts per meter, is a vector field that can be defined everywhere, except at the location of point charges. It is defined as the electrostatic force F → in newtons on a hypothetical small test charge at the point due to Coulomb's Law, divided by the magnitude of the charge q in coulombs E → = F → q Electric field lines are useful for visualizing the electric field. Field lines terminate on negative charge, they are parallel to the direction of the electric field at each point, the density of these field lines is a measure of the magnitude of the electric field at any given point. Consider a collection of N particles of charge Q i, located at points r → i, the electric field at r → is: E → =
Electric dipole moment
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 system's overall polarity. The SI units for electric dipole moment are coulomb-meter. Theoretically, an electric dipole is defined by the first-order term of the multipole expansion; this is unrealistic. However, because the charge separation is small compared to everyday lengths, the error introduced by treating real dipoles like they are theoretically perfect is negligible; the dipole's direction points from the negative charge towards the positive charge. In physics the dimensions of a massive object can be ignored and can be treated as a pointlike object, i.e. a point particle. 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 electric 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 center of the dipole, leading to a factor of two in the definition. A stronger mathematical definition is to use vector algebra, since a quantity with magnitude and direction, like the dipole moment of two point charges, can be expressed in vector form p = q d where d is the displacement vector pointing from the negative charge to the positive charge; the electric dipole moment vector p points from the negative charge to the positive charge. An idealization of this two-charge 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 dipole moment, the symbol "×" refers to the vector cross product. The field vector and the dipole vector define a plane, the torque is directed normal to that plane with the direction given by the right-hand rule. A dipole oriented co- or anti-parallel to the direction in which a non-uniform electric field is increasing will experience a torque, as well as 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. More for a continuous distribution of charge confined to a volume V, the corresponding expression for the dipole moment is: p = ∫ V ρ d 3 r 0, where r locates the point of observation and d3r0 denotes an elementary volume in V. For an array of point charges, the charge density becomes a sum of Dirac delta functions: ρ = ∑ i = 1 N q i δ, where each ri is a vector from some reference point to the charge qi.
Substitution into the above integration formula provides: p = ∑ i = 1 N q i ∫ V δ d 3 r 0 = ∑ i = 1 N q i. This expression is equivalent to the previous expression in the case of charge neutrality and N = 2. For two opposite charges, denoting the location of the positive charge of the pair as r+ and the location of the negative charge as r−: p = q 1 + q 2 ( r
Magnetic field
A magnetic field is a vector field that describes the magnetic influence of electric charges in relative motion and magnetized materials. Magnetic fields are observed from subatomic particles to galaxies. In everyday life, the effects of magnetic fields are seen in permanent magnets, which pull on magnetic materials and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field vary with location; as such, it is an example of a vector field. The term'magnetic field' is used for two distinct but related fields denoted by the symbols B and H. In the International System of Units, H, magnetic field strength, is measured in the SI base units of ampere per meter. B, magnetic flux density, is measured in tesla, equivalent to newton per meter per ampere.
H and B differ in. In a vacuum, B and H are the same aside from units. Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. Magnetic fields and electric fields are interrelated, are both components of the electromagnetic force, one of the four fundamental forces of nature. Magnetic fields are used throughout modern technology in electrical engineering and electromechanics. Rotating magnetic fields are used in both electric generators; the interaction of magnetic fields in electric devices such as transformers is studied in the discipline of magnetic circuits. Magnetic forces give information about the charge carriers in a material through the Hall effect; the Earth produces its own magnetic field, which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass. Although magnets and magnetism were studied much earlier, the research of magnetic fields began in 1269 when French scholar Petrus Peregrinus de Maricourt mapped out the magnetic field on the surface of a spherical magnet using iron needles.
Noting that the resulting field lines crossed at two points he named those points'poles' in analogy to Earth's poles. He clearly articulated the principle that magnets always have both a north and south pole, no matter how finely one slices them. Three centuries William Gilbert of Colchester replicated Petrus Peregrinus' work and was the first to state explicitly that Earth is a magnet. Published in 1600, Gilbert's 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' and magnetism is due to small pairs of north/south magnetic poles. Three discoveries in 1820 challenged this foundation of magnetism, though.
Hans Christian Ørsted demonstrated that a current-carrying wire is surrounded by a circular magnetic field. André-Marie Ampère showed that parallel wires with currents attract one another if the currents are in the same direction and repel if they are in opposite directions. Jean-Baptiste Biot and Félix Savart announced empirical results about the forces that a current-carrying long, straight wire exerted on a small magnet, determining that the forces were inversely proportional to the perpendicular distance from the wire to the magnet. Laplace deduced, but did not publish, a law of force based on the differential action of a differential section of the wire, which became known as the Biot–Savart law. Extending these experiments, Ampère published his own successful model of magnetism in 1825. In it, he showed the equivalence of electrical currents to magnets and proposed that magnetism is due to perpetually flowing loops of current instead of the dipoles of magnetic charge in Poisson's model.
This has the additional benefit of explaining. Further, Ampère derived both Ampère's force law describing the force between two currents and Ampère's law, like the Biot–Savart law described the magnetic field generated by a steady current. 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, he described this phenomenon in. Franz Ernst Neumann proved that, for a moving conductor in a magnetic field, induction is a consequence of Ampère's force law. In the process, he introduced the magnetic vector potential, shown to be equivalent to the underlying mechanism proposed by Faraday. In 1850, Lord Kelvin known as William Thomson, distinguished between two magnetic fields now denoted H and B; the former applied to the latter to Ampère's model and induction. Further, he derived how H and B relate to each other
Electromagnetism
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 exhibits electromagnetic fields such as electric fields, magnetic fields, light, is one of the four fundamental interactions in nature; the other three fundamental interactions are the strong interaction, the weak interaction, gravitation. At high energy the weak force and electromagnetic force are unified as a single electroweak force. Electromagnetic phenomena are defined in terms of the electromagnetic force, sometimes called the Lorentz force, which includes both electricity and magnetism as different manifestations of the same phenomenon; the electromagnetic force plays a major role in determining the internal properties of most objects encountered in daily life. Ordinary matter takes its form as a result of intermolecular forces between individual atoms and molecules in matter, is a manifestation of the electromagnetic force.
Electrons are bound by the electromagnetic force to atomic nuclei, their orbital shapes and their influence on nearby atoms with their electrons is described by quantum mechanics. The electromagnetic force governs all chemical processes, 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 and electric current. In Faraday's law, magnetic fields are associated with electromagnetic induction and magnetism, Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents; the theoretical implications of electromagnetism the establishment of the speed of light based on properties of the "medium" of propagation, led to the development of special relativity by Albert Einstein in 1905. Electricity and magnetism were considered to be two separate forces; this view changed, with the publication of James Clerk Maxwell's 1873 A Treatise on Electricity and Magnetism in which the interactions of positive and negative charges were shown to be mediated by one force.
There are four main effects resulting from these interactions, all of which have been demonstrated by experiments: Electric charges attract or repel one another with a force inversely proportional to the square of the distance between them: unlike charges attract, like ones repel. 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 circumferential 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 magnetic field, or a magnet is moved towards or away from it. While preparing for an evening 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 magnetic north when the electric current from the battery he was using was switched on and off.
This deflection convinced him that magnetic fields radiate from all sides of a wire carrying an electric current, just as light and heat do, that it confirmed a direct relationship between electricity and magnetism. At the time of discovery, Ørsted did not suggest any satisfactory explanation of the phenomenon, nor did he try to represent the phenomenon in a mathematical framework. However, three months he began more intensive investigations. Soon thereafter he published his findings, proving that an electric current produces a magnetic field as it flows through a wire; the CGS unit of magnetic induction is named in honor of his contributions to the field of electromagnetism. His findings resulted in intensive research throughout the scientific community in electrodynamics, they influenced French physicist André-Marie Ampère's developments of a single mathematical form to represent the magnetic forces between current-carrying conductors. Ørsted's discovery represented a major step toward a unified concept of energy.
This unification, observed by Michael Faraday, extended by James Clerk Maxwell, reformulated by Oliver Heaviside and Heinrich Hertz, is one of the key accomplishments of 19th century mathematical physics. It has had far-reaching consequences, one of, the understanding of the nature of light. Unlike what was proposed by the electromagnetic theory of that time and other electromagnetic waves are at present seen as taking the form of quantized, self-propagating oscillatory electromagnetic field disturbances called photons. Different frequencies of oscillation give rise to the different forms of electromagnetic radiation, from radio waves at the lowest frequencies, to visible light at intermediate frequencies, to gamma rays at the highest frequencies. Ørsted was not the only person to examine the relationship between magnetism. In 1802, Gian Domenico Romagnosi, an Italian legal scholar, deflected a magnetic needle using a Voltaic pile; the factual setup of the experiment is not clear, so if current flew across the needle or not.
An account of the discovery was published in 1802 in an Italian newspaper, but it was overlooked by the contemporary scientific community, because Romagnosi did not belong to this community. An earlier, neglected, connec
Magnetism
Magnetism is a class of physical phenomena that are mediated by magnetic fields. Electric currents and the magnetic moments of elementary particles give rise to a magnetic field, which acts on other currents and magnetic moments; the most familiar effects occur in ferromagnetic materials, which are attracted by magnetic fields and can be magnetized to become permanent magnets, producing magnetic fields themselves. Only a few substances are ferromagnetic; the prefix ferro- refers to iron, because permanent magnetism was first observed in lodestone, a form of natural iron ore called magnetite, Fe3O4. Although ferromagnetism is responsible for most of the effects of magnetism encountered in everyday life, all other materials are influenced to some extent by a magnetic field, by several other types of magnetism. Paramagnetic substances such as aluminum and oxygen are weakly attracted to an applied magnetic field; the force of a magnet on paramagnetic and antiferromagnetic materials is too weak to be felt, can be detected only by laboratory instruments, so in everyday life these substances are described as non-magnetic.
The magnetic state of a material depends on temperature and other variables such as pressure and the applied magnetic field. A material may exhibit more than one form of magnetism as these variables change; as with magnetising a magnet, demagnetising a magnet is possible. "Passing an alternate current, or hitting a heated magnet in an east west direction are ways of demagnetising a magnet", quotes Sreekethav. Magnetism was first discovered in the ancient world, when people noticed that lodestones magnetized pieces of the mineral magnetite, could attract iron; the word magnet comes from the Greek term μαγνῆτις λίθος magnētis lithos, "the Magnesian stone, lodestone." 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. The ancient Indian medical text Sushruta Samhita describes using magnetite to remove arrows embedded in a person's body. In ancient China, the earliest literary reference to magnetism lies in a 4th-century BC book named after its author, The Sage of Ghost Valley.
The 2nd-century BC annals, Lüshi Chunqiu 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: "A lodestone attracts a needle." The 11th-century Chinese scientist Shen Kuo was the first person to write—in the Dream Pool Essays—of the magnetic needle compass and that it improved the accuracy of navigation by employing the astronomical concept of true north. 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, the first extant treatise describing the properties of magnets. In 1282, the properties of magnets and the dry compasses were discussed by Al-Ashraf, a Yemeni physicist and geographer.
In 1600, William Gilbert published his De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure. 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 that this was the reason compasses pointed north. An understanding of the relationship between electricity and magnetism began in 1819 with work by Hans Christian Ørsted, a professor at the University of Copenhagen, who discovered by the accidental twitching of a compass needle near a wire that an electric current could create a magnetic field; this landmark experiment is known as Ørsted's Experiment. Several other experiments followed, with André-Marie Ampère, who in 1820 discovered that the magnetic field circulating in a closed-path was related to the current flowing through the perimeter of the path. James Clerk Maxwell synthesized and expanded these insights into Maxwell's equations, unifying electricity and optics into the field of electromagnetism.
In 1905, Einstein used these laws in motivating his theory of special relativity, requiring that the laws held true in all inertial reference frames. Electromagnetism has continued to develop into the 21st century, being incorporated into the more fundamental theories of gauge theory, quantum electrodynamics, electroweak theory, the standard model. Magnetism, at its root, arises from two sources: Electric current. Spin magnetic moments of elementary particles; the magnetic properties of materials are due to the magnetic moments of their atoms' orbiting electrons. The magnetic moments of the nuclei of atoms are thousands of times smaller than the electro
Magnetic moment
The magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include: loops of electric current, permanent magnets, elementary particles, various molecules, many astronomical objects. More the term magnetic moment refers to a system's magnetic dipole moment, the component of the magnetic moment that can be represented by an equivalent magnetic dipole: a magnetic north and south pole separated by a small distance; the magnetic dipole component is sufficient for large enough distances. Higher order terms may be needed in addition to the dipole moment for extended objects; the magnetic dipole moment of an object is defined in terms of the torque that object experiences in a given magnetic field. The same applied magnetic field creates larger torques on objects with larger magnetic moments; the strength of this torque depends not only on the magnitude of the magnetic moment but on its orientation relative to the direction of the magnetic field.
The magnetic moment may be considered, therefore. The direction of the magnetic moment points from the south to north pole of the magnet; the magnetic field of a magnetic dipole is proportional to its magnetic dipole moment. The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, decreases as the inverse cube of the distance from the object; the magnetic moment can be defined as a vector relating the aligning torque on the object from an externally applied magnetic field to the field vector itself. The relationship is given by: τ = m × B where τ is the torque acting on the dipole, B is the external magnetic field, m is the magnetic moment; this definition is based on how one could, in principle, measure the magnetic moment of an unknown sample. For a current loop, this definition leads to the magnitude of the magnetic dipole moment equaling the product of the current times the area of the loop. Further, this definition allows the calculation of the expected magnetic moment for any known macroscopic current distribution.
An alternative definition is useful for thermodynamics calculations of the magnetic moment. In this definition, the magnetic dipole moment of a system is the negative gradient of its intrinsic energy, with respect to external magnetic field: m = − x ^ ∂ U i n t ∂ B x − y ^ ∂ U i n t ∂ B y − z ^ ∂ U i n t ∂ B z. Generically, the intrinsic energy includes the self-field energy of the system plus the energy of the internal workings of the system. For example, for a hydrogen atom in a 2p state in an external field, the self-field energy is negligible, so the internal energy is the eigenenergy of the 2p state, which includes Coulomb potential energy and the kinetic energy of the electron; the interaction-field energy between the internal dipoles and external fields is not part of this internal energy. The unit for magnetic moment in International System of Units base units is A⋅m2, where A is ampere and m is meter; this unit has equivalents in other SI derived units including: A ⋅ m 2 = N ⋅ m T = J T, where N is newton, T is tesla, J is joule.
Although torque and energy are dimensionally equivalent, torques are never expressed in units of energy. In the CGS system, there are several different sets of electromagnetism units, of which the main ones are ESU, EMU. Among these, there are two alternative units of magnetic dipole moment: 1 statA ⋅ cm 2 = 3.33564095 × 10 − 14 A ⋅ m 2 1 erg G = 10 − 3 A ⋅ m 2,where statA is statamperes, cm is centimeters, erg is ergs, G is gauss. The ratio of these two non-equivalent CGS units is equal to the speed of light in free space, expressed in cm⋅s−1. All formula
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