Electromagnetic or magnetic induction is the production of an
electromotive force (i.e., voltage) across an electrical conductor in
a changing magnetic field.
Part of a series of articles about Electromagnetism Electricity Magnetism Electrostatics Electric charge Static electricity Electric field Conductor Insulator Triboelectricity Electrostatic discharge Induction Coulomb's law Gauss's law Electric flux / potential energy Electric dipole moment Polarization density Magnetostatics Ampère's law Magnetic field Magnetization Magnetic flux Biot–Savart law Magnetic dipole moment Gauss's law for magnetism Electrodynamics
Mathematical descriptions of the electromagnetic field Electrical network Electric current Electric potential Voltage Resistance Ohm's law Series circuit Parallel circuit Direct current Alternating current Electromotive force Capacitance Inductance Impedance Resonant cavities Waveguides Covariant formulation Electromagnetic tensor (stress–energy tensor) Four-current Electromagnetic four-potential Scientists Ampère Coulomb Faraday Gauss Heaviside Henry Hertz Lorentz Maxwell Tesla Volta Weber Ørsted v t e Contents 1 History 2 Theory 2.1
3 Applications 3.1 Electrical generator 3.2 Electrical transformer 3.2.1 Current clamp 3.3 Magnetic flow meter 4 Eddy currents 4.1
5 See also 6 References 7 Further reading 8 External links History[edit] A diagram of Faraday's iron ring apparatus. Change in the magnetic flux of the left coil induces a current in the right coil.[2] Faraday's disk (see homopolar generator)
A solenoid The longitudinal cross section of a solenoid with a constant electrical current running through it. The magnetic field lines are indicated, with their direction shown by arrows. The magnetic flux corresponds to the 'density of field lines'. The magnetic flux is thus densest in the middle of the solenoid, and weakest outside of it.
Φ B = ∫ Σ B ⋅ d A , displaystyle Phi _ mathrm B =int limits _ Sigma mathbf B cdot dmathbf A , where dA is an element of the surface Σ enclosed by the wire loop, B is the magnetic field. The dot product B·dA corresponds to an infinitesimal amount of magnetic flux. In more visual terms, the magnetic flux through the wire loop is proportional to the number of magnetic flux lines that pass through the loop. When the flux through the surface changes, Faraday's law of induction says that the wire loop acquires an electromotive force (EMF).[note 1] The most widespread version of this law states that the induced electromotive force in any closed circuit is equal to the rate of change of the magnetic flux enclosed by the circuit:[16][17] E = − d Φ B d t
displaystyle mathcal E =- dPhi _ mathrm B over dt , where E displaystyle mathcal E is the EMF and ΦB is the magnetic flux. The direction of the
electromotive force is given by
E = − N d Φ B d t displaystyle mathcal E =-N dPhi _ mathrm B over dt Generating an EMF through a variation of the magnetic flux through the surface of a wire loop can be achieved in several ways: the magnetic field B changes (e.g. an alternating magnetic field, or moving a wire loop towards a bar magnet where the B field is stronger), the wire loop is deformed and the surface Σ changes, the orientation of the surface dA changes (e.g. spinning a wire loop into a fixed magnetic field), any combination of the above Maxwell–Faraday equation[edit]
See also:
E displaystyle mathcal E in a wire loop encircling a surface Σ, and the electric field E in the wire is given by E = ∮ ∂ Σ E ⋅ d ℓ displaystyle mathcal E =oint _ partial Sigma mathbf E cdot d boldsymbol ell where dℓ is an element of contour of the surface Σ, combining this with the definition of flux Φ B = ∫ Σ B ⋅ d A , displaystyle Phi _ mathrm B =int limits _ Sigma mathbf B cdot dmathbf A , we can write the integral form of the Maxwell–Faraday equation ∮ ∂ Σ E ⋅ d ℓ = − d d t ∫ Σ B ⋅ d A displaystyle oint _ partial Sigma mathbf E cdot d boldsymbol ell =- frac d dt int _ Sigma mathbf B cdot dmathbf A It is one of the four Maxwell's equations, and therefore plays a
fundamental role in the theory of classical electromagnetism.
Faraday's law and relativity[edit]
Faraday's law describes two different phenomena: the motional EMF
generated by a magnetic force on a moving wire (see Lorentz force),
and the transformer EMF generated by an electric force due to a
changing magnetic field (due to the differential form of the
Maxwell–Faraday equation).
Current clamp
Electric generators
Electromagnetic forming
Graphics tablet
Electrical generator[edit] Rectangular wire loop rotating at angular velocity ω in radially outward pointing magnetic field B of fixed magnitude. The circuit is completed by brushes making sliding contact with top and bottom discs, which have conducting rims. This is a simplified version of the drum generator. Main article: Electric generator
The EMF generated by
A current clamp Main article: Current clamp A current clamp is a type of transformer with a split core which can be spread apart and clipped onto a wire or coil to either measure the current in it or, in reverse, to induce a voltage. Unlike conventional instruments the clamp does not make electrical contact with the conductor or require it to be disconnected during attachment of the clamp. Magnetic flow meter[edit] Main article: Magnetic flow meter Faraday's law is used for measuring the flow of electrically conductive liquids and slurries. Such instruments are called magnetic flow meters. The induced voltage ℇ generated in the magnetic field B due to a conductive liquid moving at velocity v is thus given by: E = − B ℓ v , displaystyle mathcal E =-Bell v, where ℓ is the distance between electrodes in the magnetic flow meter. Eddy currents[edit] Main article: Eddy current Conductors (of finite dimensions) moving through a uniform magnetic field, or stationary within a changing magnetic field, will have currents induced within them. These induced eddy currents can be undesirable, since they dissipate energy in the resistance of the conductor. There are a number of methods employed to control these undesirable inductive effects. Electromagnets in electric motors, generators, and transformers do not use solid metal, but instead use thin sheets of metal plate, called laminations. These thin plates reduce the parasitic eddy currents, as described below. Inductive coils in electronics typically use magnetic cores to minimize parasitic current flow. They are a mixture of metal powder plus a resin binder that can hold any shape. The binder prevents parasitic current flow through the powdered metal.
Eddy currents occur when a solid metallic mass is rotated in a magnetic field, because the outer portion of the metal cuts more lines of force than the inner portion, hence the induced electromotive force not being uniform, tends to set up currents between the points of greatest and least potential. Eddy currents consume a considerable amount of energy and often cause a harmful rise in temperature.[25] Only five laminations or plates are shown in this example, so as to show the subdivision of the eddy currents. In practical use, the number of laminations or punchings ranges from 40 to 66 per inch, and brings the eddy current loss down to about one percent. While the plates can be separated by insulation, the voltage is so low that the natural rust/oxide coating of the plates is enough to prevent current flow across the laminations.[25] This is a rotor approximately 20mm in diameter from a DC motor used in a CD player. Note the laminations of the electromagnet pole pieces, used to limit parasitic inductive losses. Parasitic induction within conductors[edit] In this illustration, a solid copper bar conductor on a rotating armature is just passing under the tip of the pole piece N of the field magnet. Note the uneven distribution of the lines of force across the copper bar. The magnetic field is more concentrated and thus stronger on the left edge of the copper bar (a,b) while the field is weaker on the right edge (c,d). Since the two edges of the bar move with the same velocity, this difference in field strength across the bar creates whorls or current eddies within the copper bar.[25] High current power-frequency devices, such as electric motors, generators and transformers, use multiple small conductors in parallel to break up the eddy flows that can form within large solid conductors. The same principle is applied to transformers used at higher than power frequency, for example, those used in switch-mode power supplies and the intermediate frequency coupling transformers of radio receivers. See also[edit] Book: Maxwell's equations Alternator Crosstalk Faraday paradox Inductance Moving magnet and conductor problem References[edit] Notes ^ The EMF is the voltage that would be measured by cutting the wire to create an open circuit, and attaching a voltmeter to the leads. Mathematically, E displaystyle mathcal E is defined as the energy available from a unit charge that has traveled once around the wire loop.[13][14][15] References ^ Poyser, A. W. (1892).
Translated in Einstein, A. (1923). "On the Electrodynamics of Moving Bodies" (PDF). The Principle of Relativity. Jeffery, G.B.; Perret, W. (transl.). London: Methuen and Company. ^ a b c Images and reference text are from the public domain book: Hawkins Electrical Guide, Volume 1, Chapter 19: Theory of the Armature, pp. 270–273, Copyright 1917 by Theo. Audel & Co., Printed in the United States Further reading[edit] Maxwell, James Clerk (1881), A treatise on electricity and magnetism, Vol. II, Chapter III, §530, p. 178. Oxford, UK: Clarendon Press. ISBN 0-486-60637-6. External links[edit] A simple interactive Java tutorial on electromagnetic induction
National High Magnetic Field Laboratory
R. Vega Induction: Faraday's law and
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