### Paramagnetism

paramagneticparamagnetParamagnetic materials
Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, diamagnetic materials are repelled by magnetic fields and form induced magnetic fields in the direction opposite to that of the applied magnetic field. Paramagnetic materials include most chemical elements and some compounds; they have a relative magnetic permeability slightly greater than 1 (i.e., a small positive magnetic susceptibility) and hence are attracted to magnetic fields.

### Superconductivity

superconductingsuperconductorsuperconductors
Similarly, at a fixed temperature below the critical temperature, superconducting materials cease to superconduct when an external magnetic field is applied which is greater than the critical magnetic field. This is because the Gibbs free energy of the superconducting phase increases quadratically with the magnetic field while the free energy of the normal phase is roughly independent of the magnetic field.

### Wilhelm Eduard Weber

Wilhelm WeberWeberWilliam Weber
This also led to Weber's development of his theory of electrodynamics. Also, the first usage of the letter "c" to denote the speed of light was in an 1856 paper by Kohlrausch and Weber. The SI unit of magnetic flux, the weber (symbol: Wb) is named after him. * German inventors and discoverers * * – obituary. – Telegraph of Weber and Gauss (with pictures). – Telegraph of Weber and Gauss (with pictures). Biography and bibliography in the Virtual Laboratory of the Max Planck Institute for the History of Science. Wilhelm Weber's Works Translated into English A bibliography compiled by A.K.T. Assis in 21st Century Science and Technology 2009-2010.

### Euclidean vector

Other physical vectors, such as the electric and magnetic field, are represented as a system of vectors at each point of a physical space; that is, a vector field. Examples of quantities that have magnitude and direction but fail to follow the rules of vector addition are angular displacement and electric current. Consequently, these are not vectors. In the Cartesian coordinate system, a bound vector can be represented by identifying the coordinates of its initial and terminal point. For instance, the points A = (1, 0, 0) and B = (0, 1, 0) in space determine the bound vector pointing from the point x = 1 on the x-axis to the point y = 1 on the y-axis.

### Type-II superconductor

Type II superconductortype-II superconductorstype-II
In the vortex state, a phenomenon known as flux pinning, where a superconductor is pinned in space above a magnet, becomes possible. This is not possible with type-I superconductors, since they cannot be penetrated by magnetic fields. Since the superconductor is pinned above the magnet away from any surfaces, there is the potential for a frictionless joint. The worth of flux pinning is seen through many implementations such as lifts, frictionless joints, and transportation. The thinner the superconducting layer, the stronger the pinning that occurs when exposed to magnetic fields. Type-II superconductors are usually made of metal alloys or complex oxide ceramics.

### Magnetization

magnetizedmagnetisationbound current
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. The origin of the magnetic moments responsible for magnetization can be either microscopic electric currents resulting from the motion of electrons in atoms, or the spin of the electrons or the nuclei. Net magnetization results from the response of a material to an external magnetic field. Paramagnetic materials have a weak induced magnetization in a magnetic field, which disappears when the magnetic field is removed.

### Moving magnet and conductor problem

conductor moving in the field of a magnetelectric conductor moving with respect to a magnet
Unprimed quantities correspond to the rest frame of the magnet, while primed quantities correspond to the rest frame of the conductor. Let v be the velocity of the conductor, as seen from the magnet frame. In the rest frame of the magnet, the magnetic field is some fixed field B(r), determined by the structure and shape of the magnet. The electric field is zero. In general, the force exerted upon a particle of charge q in the conductor by the electric field and magnetic field is given by (SI units): where q is the charge on the particle, \mathbf{v} is the particle velocity and F is the Lorentz force.

### Lenz's law

his important lawlawLenz effect
Lenz's law, named after the physicist Emil Lenz (pronounced ) who formulated it in 1834, states that the direction of the current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field. It is a qualitative law that specifies the direction of induced current, but states nothing about its magnitude. Lenz's law explains the direction of many effects in electromagnetism, such as the direction of voltage induced in an inductor or wire loop by a changing current, or the drag force of eddy currents exerted on moving objects in a magnetic field.

### Search coil magnetometer

search coilsearch-coil magnetometerinduction magnetometer
The coil is placed in the magnetic field to be measured and quickly withdrawn to a region of space with a negligible magnetic field. As the search coil moves the magnetic flux linked with the coil changes. This induces a current in the coil which can be registered on the galvanometer. Since induced current is directly proportional to rate of change of flux linkage and assuming the coil is removed from the magnetic field very quickly, the maximum current measured by the ammeter is proportional to the magnetic field. The search coil can be calibrated by repeating this in a known magnetic field.

### Ampère's circuital law

Ampère's lawAmpere's lawAmpere's circuital law
Treating free charges separately from bound charges, The equation including Maxwell's correction in terms of the H -field is (the H -field is used because it includes the magnetization currents, so J M does not appear explicitly, see [[Magnetic Field#Physical interpretation of the H field| H -field]] and also Note): (integral form), where H is the [[magnetic field|magnetic H field]] (also called "auxiliary magnetic field", "magnetic field intensity", or just "magnetic field"), D is the electric displacement field, and J f is the enclosed conduction current or free current density.

### Electric generator

generatorgeneratorselectrical generator
In particular, inductance can be added to allow for the machine's windings and magnetic leakage flux, but a full representation can become much more complex than this. Dynamos generate pulsing direct current through the use of a commutator. Alternators generate alternating current. Rotor: The rotating part of an electrical machine. Stator: The stationary part of an electrical machine, which surrounds the rotor. Field winding or field (permanent) magnets: The magnetic field producing component of an electrical machine. The magnetic field of the dynamo or alternator can be provided by either wire windings called field coils or permanent magnets.

### A Dynamical Theory of the Electromagnetic Field

Dynamical Theory of the Electromagnetic Fieldelectromagnetic theory of lighttheory
A Treatise on Electricity and Magnetism. "On Physical Lines of Force". Gauge theory.

### Fleming's left-hand rule for motors

Fleming's left hand ruleFleming's LawFleming's left hand rule for motors
If an external magnetic field is applied horizontally, so that it crosses the flow of electrons (in the wire conductor, or in the electron beam), the two magnetic fields will interact. Michael Faraday introduced a visual analogy for this, in the form of imaginary magnetic lines of force: those in the conductor form concentric circles round the conductor; those in the externally applied magnetic field run in parallel lines.

### Maxwell stress tensor

Maxwell tensorelectromagnetic stress tensorMaxwell
For the case of nonlinear materials (such as magnetic iron with a BH-curve), the nonlinear Maxwell stress tensor must be used. In physics, the Maxwell stress tensor is the stress tensor of an electromagnetic field. As derived above in SI units, it is given by: :, where ε 0 is the electric constant and μ 0 is the magnetic constant, E is the electric field, B is the magnetic field and δ ij is Kronecker's delta. In Gaussian cgs unit, it is given by: :, where H is the magnetizing field.

### Quantum field theory

quantum field theoriesquantum fieldquantum theory
The theory of classical electromagnetism was completed in 1862 with Maxwell's equations, which described the relationship between the electric field, the magnetic field, electric current, and electric charge. Maxwell's equations implied the existence of electromagnetic waves, a phenomenon whereby electric and magnetic fields propagate from one spatial point to another at a finite speed, which turns out to be the speed of light. Action-at-a-distance was thus conclusively refuted. Despite the enormous success of classical electromagnetism, it was unable to account for the discrete lines in atomic spectra, nor for the distribution of blackbody radiation in different wavelengths.

### Dynamo theory

dynamogeodynamogeodynamo effect
Rotating magnetic field. Secular variation.

### Right-hand rule

right hand ruleright-handedright hand grip rule
A magnetic field, the position of the point where it is determined, and the electric current (or change in electric flux) that causes it. A magnetic field in a coil of wire and the electric current in the wire. The force of a magnetic field on a charged particle, the magnetic field itself, and the velocity of the object. The vorticity at any point in the field of flow of a fluid. The induced current from motion in a magnetic field (known as Fleming's right-hand rule). The x, y and z unit vectors in a Cartesian coordinate system can be chosen to follow the right-hand rule. Right-handed coordinate systems are often used in rigid body and kinematics. Chirality (mathematics).

### Magnetar

magnetarscigar shapedetected in March 1979
But another theory is that they simply result from the collapse of stars with unusually high magnetic fields. When in a supernova, a star collapses to a neutron star, and its magnetic field increases dramatically in strength. Halving a linear dimension increases the magnetic field fourfold. Duncan and Thompson calculated that when the spin, temperature and magnetic field of a newly formed neutron star falls into the right ranges, a dynamo mechanism could act, converting heat and rotational energy into magnetic energy and increasing the magnetic field, normally an already enormous 10 8 teslas, to more than 10 11 teslas (or 10 15 gauss). The result is a magnetar.

### Orders of magnitude (magnetic field)

10,000 nanoteslas2.1526fields
This page lists examples of magnetic induction B in teslas and gauss produced by various sources, grouped by orders of magnitude. Note: These examples attempt to make the measuring point clear, usually the surface of the item mentioned. Traditionally, magnetizing field H, is measured in amperes per meter. Magnetic induction B (also known as magnetic flux density) has the SI unit tesla [T or Wb/m 2 ]. One tesla is equal to 10 4 gauss. Magnetic field drops off as the cube of the distance from a dipole source.

### Solenoidal vector field

solenoidaldivergence-freesolenoidal field
. * The magnetic field B (see Maxwell's equations). The velocity field of an incompressible fluid flow. The vorticity field. The electric field E in neutral regions (\rho_e = 0). The current density J where the charge density is unvarying,. The magnetic vector potential A in Coulomb gauge. Longitudinal and transverse vector fields. Stream function. Conservative vector field.

### Magnetic dipole

dipolemagnetic dipoles
A magnetic dipole is the limit of either a closed loop of electric current or a pair of poles as the size of the source is reduced to zero while keeping the magnetic moment constant. It is a magnetic analogue of the electric dipole, but the analogy is not perfect. In particular, a magnetic monopole, the magnetic analogue of an electric charge, has never been observed. Moreover, one form of magnetic dipole moment is associated with a fundamental quantum property—the spin of elementary particles. The magnetic field around any magnetic source looks increasingly like the field of a magnetic dipole as the distance from the source increases.

### Nikola Tesla

TeslaNicola TeslaTesla, Nikola
The magnetic armature vibrated up and down at high speed, producing an alternating magnetic field. This induced alternating electric current in the wire coils located adjacent. It did away with the complicated parts of a steam engine/generator, but never caught on as a feasible engineering solution to generate electricity. At the beginning of 1893, Westinghouse engineer Benjamin Lamme had made great progress developing an efficient version of Tesla's induction motor, and Westinghouse Electric started branding their complete polyphase AC system as the "Tesla Polyphase System". They believed that Tesla's patents gave them patent priority over other AC systems.

### International Electrotechnical Commission

IECInternational Electrotechnical Commission (IEC)(IEC)
All electrotechnologies are covered by IEC Standards, including energy production and distribution, electronics, magnetics and electromagnetics, electroacoustics, multimedia, telecommunication and medical technology, as well as associated general disciplines such as terminology and symbols, electromagnetic compatibility, measurement and performance, dependability, design and development, safety and the environment. The first International Electrical Congress took place in 1881 at the International Exposition of Electricity, held in Paris. At that time the International System of Electrical and Magnetic Units was agreed to.

### Field (physics)

fieldfieldsfield theory
The force exerted by I on a nearby charge q with velocity v is : where B(r) is the magnetic field, which is determined from I by the Biot–Savart law: : The magnetic field is not conservative in general, and hence cannot usually be written in terms of a scalar potential. However, it can be written in terms of a vector potential, A(r): : In general, in the presence of both a charge density ρ(r, t) and current density J(r, t), there will be both an electric and a magnetic field, and both will vary in time. They are determined by Maxwell's equations, a set of differential equations which directly relate E and B to ρ and J.

### Eddy current

eddy currentseddyeddy-current
Due to Ampere's circuital law each of these circular currents creates a counter magnetic field ( blue arrows ), which due to Lenz's law opposes the change in magnetic field which caused it, exerting a drag force on the sheet. At the leading edge of the magnet (left side) by the right hand rule the counterclockwise current creates a magnetic field pointed up, opposing the magnet's field, causing a repulsive force between the sheet and the leading edge of the magnet.