Coulomb's law

Coulomb forceelectrostatic forceCoulomb interaction
This extra part of the force is called the magnetic force, and is described by magnetic fields. For slow movement, the magnetic force is minimal and Coulomb's law can still be considered approximately correct, but when the charges are moving more quickly in relation to each other, the full electrodynamic rules (incorporating the magnetic force) must be considered. In simple terms, the Coulomb potential derives from the QED Lagrangian as follows. The Lagrangian of quantum electrodynamics is normally written in natural units, but in SI units, it is: where the covariant derivative (in SI units) is: where g is the gauge coupling parameter.

Induction motor

asynchronous motorasynchronousinduction motors
The rotating magnetic flux induces currents in the windings of the rotor, in a manner similar to currents induced in a transformer's secondary winding(s). The induced currents in the rotor windings in turn create magnetic fields in the rotor that react against the stator field. Due to Lenz's Law, the direction of the magnetic field created will be such as to oppose the change in current through the rotor windings. The cause of induced current in the rotor windings is the rotating stator magnetic field, so to oppose the change in rotor-winding currents the rotor will start to rotate in the direction of the rotating stator magnetic field.

Current density

current densitieselectric current densitycurrent
Aside from the material properties themselves, the application of magnetic fields can alter conductive behaviour. Currents arise in materials when there is a non-uniform distribution of charge.

Constitutive equation

constitutive relationconstitutive equationsconstitutive model
+Definitions (Electrical/magnetic properties of matter). Electrical resistance. R. R = V/I. Ω = V⋅A −1 = J⋅s⋅C −2. [M][L] 2 [T] −3 [I] −2. Resistivity. \rho = RA/l. Ω⋅m. [M] 2 [L] 2 [T] −3 [I] −2. Resistivity temperature coefficient, linear temperature dependence. K −1. [Θ] −1. Electrical conductance|| G. G = 1/R. S = Ω −1. [M] −1 [L] −2 [T] 3 [I] 2. Electrical conductivity|| σ. Ω −1 ⋅m −1. [M] −2 [L] −2 [T] 3 [I] 2. Magnetic reluctance. R, R m, \mathcal{R}. A⋅Wb −1 = H −1. [M] −1 [L] −2 [T] 2. Magnetic permeance. P, P m, Λ, \mathcal{P}. Wb⋅A −1 = H. [M][L] 2 [T] −2. }. Magnetic reluctance. R, R m, \mathcal{R}. A⋅Wb −1 = H −1. [M] −1 [L] −2 [T] 2. Magnetic permeance. P, P m, Λ, \mathcal{P}.

Electromagnetic tensor

electromagnetic field tensorfield strength tensorelectromagnetic field strength tensor
In contravariant matrix form, : The covariant form is given by index lowering, From now on in this article, when the electric or magnetic fields are mentioned, a Cartesian coordinate system is assumed, and the electric and magnetic fields are with respect to the coordinate system's reference frame, as in the equations above. The matrix form of the field tensor yields the following properties: This tensor simplifies and reduces Maxwell's equations as four vector calculus equations into two tensor field equations.

Work (physics)

workmechanical workwork-energy theorem
The magnetic force on a charged particle is F = qv × B, where q is the charge, v is the velocity of the particle, and B is the magnetic field. The result of a cross product is always perpendicular to both of the original vectors, so F ⊥ v. The dot product of two perpendicular vectors is always zero, so the work W = F ⋅ v = 0, and the magnetic force does not do work. It can change the direction of motion but never change the speed. For moving objects, the quantity of work/time (power) is integrated along the trajectory of the point of application of the force.

Classical electromagnetism

classical electrodynamicselectrodynamicsclassical
Weber electrodynamics. Wheeler–Feynman absorber theory. Leontovich boundary condition.


tokamakselectron cyclotron resonance heatingadvanced tokamak
The magnetic fields compress the gas in the chamber, increasing the collisions between nuclei. When heated to fusion temperatures, the electrons in atoms disassociate, resulting in a fluid of nuclei and electrons known as a plasma. Unlike electrically neutral atoms, a plasma is electrically conductive, and can, therefore, be manipulated by electrical or magnetic fields. Sakharov's concern about the electrodes led him to consider using magnetic confinement instead of electrostatic. In the case of a magnetic field, the particles will circle around the lines of force. As the particles are moving at high speed, their resulting paths look like a helix.

Synchronous motor

synchronousPermanent Magnet Synchronous Motorpermanent-magnet synchronous motor
A permanent-magnet synchronous motor (PMSM) uses permanent magnets embedded in the steel rotor to create a constant magnetic field. The stator carries windings connected to an AC supply to produce a rotating magnetic field. At synchronous speed the rotor poles lock to the rotating magnetic field. Permanent magnet synchronous motors are similar to brushless DC motors. Because of the constant magnetic field in the rotor these cannot use induction windings for starting. These motors require a variable-frequency power source to start. The main difference between a permanent magnet synchronous motor and an asynchronous motor is the rotor.


NiNi 2+ Nickel (Ni)
Nickel is a naturally magnetostrictive material, meaning that, in the presence of a magnetic field, the material undergoes a small change in length. The magnetostriction of nickel is on the order of 50 ppm and is negative, indicating that it contracts. Nickel is used as a binder in the cemented tungsten carbide or hardmetal industry and used in proportions of 6% to 12% by weight.

Solar dynamo

dynamoSolar Dynamo theorydynamo process
The process carries on continuously, and in an idealized, simplified scenario, each 11-year sunspot cycle corresponds to a change in the polarity of the Sun's large-scale magnetic field. Stellar magnetic field. Solar activity. Atmospheric dynamo.


forcesattractiveelastic force
The fact that the Earth's magnetic field is aligned closely with the orientation of the Earth's axis causes compass magnets to become oriented because of the magnetic force pulling on the needle. Through combining the definition of electric current as the time rate of change of electric charge, a rule of vector multiplication called Lorentz's Law describes the force on a charge moving in a magnetic field. The connection between electricity and magnetism allows for the description of a unified electromagnetic force that acts on a charge. This force can be written as a sum of the electrostatic force (due to the electric field) and the magnetic force (due to the magnetic field).

Virtual particle

virtualvirtual photonvirtual photons
The magnetic field between magnetic dipoles. It is caused by the exchange of virtual photons. In symmetric 3-dimensional space, this exchange results in the inverse cube law for magnetic force. Since the photon has no mass, the magnetic potential has an infinite range. Electromagnetic induction. This phenomenon transfers energy to and from a magnetic coil via a changing (electro)magnetic field. The strong nuclear force between quarks is the result of interaction of virtual gluons. The residual of this force outside of quark triplets (neutron and proton) holds neutrons and protons together in nuclei, and is due to virtual mesons such as the pi meson and rho meson.

Magnetic nanoparticles

magnetic nanoparticlebeadFerrite nanoparticles
Graphene coated cobalt nanoparticles have been used for that experiment since they exhibit a higher magnetization than Ferrite nanoparticles, which is essential for a fast and clean separation via external magnetic field. There are many applications for iron-oxide based nanoparticles in concert with magnetic resonance imaging. Magnetic CoPt nanoparticles are being used as an MRI contrast agent for transplanted neural stem cell detection. In magnetic fluid hyperthermia, nanoparticles of different types like Iron oxide, magnetite, maghemite or even gold are injected in tumor and then subjected under a high frequency magnetic field.

Magnetomotive force

In physics, the magnetomotive force (mmf) is a quantity appearing in the equation for the magnetic flux in a magnetic circuit, often called Ohm's law for magnetic circuits. It is the property of certain substances or phenomena that give rise to magnetic fields: : where Φ is the magnetic flux and R is the reluctance of the circuit.


In ideal MHD, Lenz's law dictates that the fluid is in a sense tied to the magnetic field lines. To explain, in ideal MHD a small rope-like volume of fluid surrounding a field line will continue to lie along a magnetic field line, even as it is twisted and distorted by fluid flows in the system. This is sometimes referred to as the magnetic field lines being "frozen" in the fluid. The connection between magnetic field lines and fluid in ideal MHD fixes the topology of the magnetic field in the fluid—for example, if a set of magnetic field lines are tied into a knot, then they will remain so as long as the fluid/plasma has negligible resistivity.

Magnetic potential

magnetic vector potentialvector potentialmagnetic scalar potential
The term magnetic potential can be used for either of two quantities in classical electromagnetism: the magnetic vector potential, or simply vector potential, A; and the magnetic scalar potential ψ. Both quantities can be used in certain circumstances to calculate the magnetic field B. The more frequently used magnetic vector potential is defined so that its curl is equal to the magnetic field:. Together with the electric potential φ, the magnetic vector potential can be used to specify the electric field E as well. Therefore, many equations of electromagnetism can be written either in terms of the fields E and B, or equivalently in terms of the potentials φ and A.

Magnetic hysteresis

hysteresisHysteresis loopB-H'' hysteresis curve
thumb|right|400px|[[Stoner–Wohlfarth model|Theoretical model of magnetization m against magnetic field h . Starting at the origin, the upward curve is the initial magnetization curve. The downward curve after saturation, along with the lower return curve, form the main loop. The intercepts h c and m rs are the coercivity and saturation remanence. ]] Magnetic hysteresis occurs when an external magnetic field is applied to a ferromagnet such as iron and the atomic dipoles align themselves with it. Even when the field is removed, part of the alignment will be retained: the material has become magnetized. Once magnetized, the magnet will stay magnetized indefinitely.

Quadrupole magnet

quadrupolefocusing magnetLenses
Quadrupole magnets, abbreviated as Q-magnets, consist of groups of four magnets laid out so that in the planar multipole expansion of the field, the dipole terms cancel and where the lowest significant terms in the field equations are quadrupole. Quadrupole magnets are useful as they create a magnetic field whose magnitude grows rapidly with the radial distance from its longitudinal axis. This is used in particle beam focusing. The simplest magnetic quadrupole is two identical bar magnets parallel to each other such that the north pole of one is next to the south of the other and vice versa.

Stellar magnetic field

magnetic fieldmagnetic activityactive
The magnetic fields of the host star and exoplanet do not interact, and this system is no longer believed to have a "star-planet interaction." * Alpha2 Canum Venaticorum variable. Dynamo theory. Earth's magnetic field. Fossil stellar magnetic field. Intermediate polar. Magnetic field. Peculiar star. Polar (cataclysmic variable). SX Arietis variable.

Helmholtz coil

Helmholtz coilsquadrupole field
From symmetry, the field strength at the midpoint will be twice the single coil value: Most Helmholtz coils use DC (direct) current to produce a static magnetic field. Many applications and experiments require a time-varying magnetic field. These applications include magnetic field susceptibility tests, scientific experiments, and biomedical studies (the interaction between magnetic field and living tissue). The required magnetic fields are usually either pulse or continuous sinewave. The magnetic field frequency range can be anywhere from near DC (0 Hz) to many kilohertz or even megahertz (MHz). An AC Helmholtz coil driver is needed to generate the required time-varying magnetic field.

Magnetic reconnection

reconnectionintense magnetic fieldmagnetic field line reconnection
Magnetic reconnection is a physical process occurring in highly conducting plasmas in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration. Magnetic reconnection occurs on timescales intermediate between slow resistive diffusion of the magnetic field and fast Alfvénic timescales. According to simple resistive magnetohydrodynamics (MHD) theory, reconnection happens because the plasma's electrical resistivity near the boundary layer opposes the currents necessary to sustain the change in the magnetic field.

Relativistic Heavy Ion Collider

RHICPHOBOS experimentRelativistic Heavy Ion Collider (RHIC)
Among the two larger detectors, STAR is aimed at the detection of hadrons with its system of time projection chambers covering a large solid angle and in a conventionally generated solenoidal magnetic field, while PHENIX is further specialized in detecting rare and electromagnetic particles, using a partial coverage detector system in a superconductively generated axial magnetic field. The smaller detectors have larger pseudorapidity coverage, PHOBOS has the largest pseudorapidity coverage of all detectors, and tailored for bulk particle multiplicity measurement, while BRAHMS is designed for momentum spectroscopy, in order to study the so-called "small-x" and saturation physics.


The electric charge-to-mass ratio of a particle can be measured by observing the radius of curling of its cloud-chamber track in a magnetic field. Positrons, because of the direction that their paths curled, were at first mistaken for electrons travelling in the opposite direction. Positron paths in a cloud-chamber trace the same helical path as an electron but rotate in the opposite direction with respect to the magnetic field direction due to their having the same magnitude of charge-to-mass ratio but with opposite charge and, therefore, opposite signed charge-to-mass ratios.


conservation of momentumlinear momentummomenta
In Maxwell's equations, the forces between particles are mediated by electric and magnetic fields. The electromagnetic force (Lorentz force) on a particle with charge q due to a combination of electric field E and magnetic field B is :(in SI units). It has an electric potential φ(r, t) and magnetic vector potential A(r, t) . In the non-relativistic regime, its generalized momentum is :while in relativistic mechanics this becomes : In Newtonian mechanics, the law of conservation of momentum can be derived from the law of action and reaction, which states that every force has a reciprocating equal and opposite force.