**Electromagnetic** or **magnetic induction** is the production of an electromotive force (emf) across an electrical conductor in a changing magnetic field.

Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk Maxwell mathematically described it as Faraday's law of induction. Lenz's law describes the direction of the induced field. Faraday's law was later generalized vĩ đại become the Maxwell–Faraday equation, one of the four Maxwell equations in his theory of electromagnetism.

Electromagnetic induction has found many applications, including electrical components such as inductors and transformers, and devices such as electric motors and generators.

## History

Electromagnetic induction was discovered by Michael Faraday, published in 1831.^{[3]}^{[4]} It was discovered independently by Joseph Henry in 1832.^{[5]}^{[6]}

In Faraday's first experimental demonstration (August 29, 1831), he wrapped two wires around opposite sides of an iron ring or "torus" (an arrangement similar vĩ đại a modern toroidal transformer).^{[citation needed]} Based on his understanding of electromagnets, he expected that, when current started vĩ đại flow in one wire, a sort of wave would travel through the ring and cause some electrical effect on the opposite side. He plugged one wire into a galvanometer, and watched it as he connected the other wire vĩ đại a battery. He saw a transient current, which he called a "wave of electricity", when he connected the wire vĩ đại the battery and another when he disconnected it.^{[7]} This induction was due vĩ đại the change in magnetic flux that occurred when the battery was connected and disconnected.^{[2]} Within two months, Faraday found several other manifestations of electromagnetic induction. For example, he saw transient currents when he quickly slid a bar magnet in and out of a coil of wires, and he generated a steady (DC) current by rotating a copper disk near the bar magnet with a sliding electrical lead ("Faraday's disk").^{[8]}

Faraday explained electromagnetic induction using a concept he called lines of force. However, scientists at the time widely rejected his theoretical ideas, mainly because they were not formulated mathematically.^{[9]} An exception was James Clerk Maxwell, who used Faraday's ideas as the basis of his quantitative electromagnetic theory.^{[9]}^{[10]}^{[11]} In Maxwell's model, the time varying aspect of electromagnetic induction is expressed as a differential equation, which Oliver Heaviside referred vĩ đại as Faraday's law even though it is slightly different from Faraday's original formulation and does not describe motional emf. Heaviside's version (see Maxwell–Faraday equation below) is the khuông recognized today in the group of equations known as Maxwell's equations.

In 1834 Heinrich Lenz formulated the law named after him vĩ đại describe the "flux through the circuit". Lenz's law gives the direction of the induced emf and current resulting from electromagnetic induction.

## Theory

### Faraday's law of induction and Lenz's law

Faraday's law of induction makes use of the magnetic flux Φ_{B} through a region of space enclosed by a wire loop. The magnetic flux is defined by a surface integral:^{[12]}

where *d***A** is an element of the surface Σ enclosed by the wire loop, **B** is the magnetic field. The dot product **B**·*d***A** corresponds vĩ đại an infinitesimal amount of magnetic flux. In more visual terms, the magnetic flux through the wire loop is proportional vĩ đại the number of magnetic field 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 vĩ đại the rate of change of the magnetic flux enclosed by the circuit:^{[16]}^{[17]}

where is the emf and Φ_{B} is the magnetic flux. The direction of the electromotive force is given by Lenz's law which states that an induced current will flow in the direction that will oppose the change which produced it.^{[18]} This is due vĩ đại the negative sign in the previous equation. To increase the generated emf, a common approach is vĩ đại exploit flux linkage by creating a tightly wound coil of wire, composed of *N* identical turns, each with the same magnetic flux going through them. The resulting emf is then *N* times that of one single wire.^{[19]}^{[20]}

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
*d***A**changes (e.g. spinning a wire loop into a fixed magnetic field), - any combination of the above

### Maxwell–Faraday equation

In general, the relation between the emf in a wire loop encircling a surface Σ, and the electric field **E** in the wire is given by

where *d***ℓ** is an element of contour of the surface Σ, combining this with the definition of flux

Xem thêm: định luật bảo toàn electron

we can write the integral khuông of the Maxwell–Faraday equation

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

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* this is generated by an electric force due vĩ đại a changing magnetic field (due vĩ đại the differential khuông of the Maxwell–Faraday equation). James Clerk Maxwell drew attention vĩ đại the separate physical phenomena in 1861.^{[21]}^{[22]} This is believed vĩ đại be a unique example in physics of where such a fundamental law is invoked vĩ đại explain two such different phenomena.^{[23]}

Albert Einstein noticed that the two situations both corresponded vĩ đại a relative movement between a conductor and a magnet, and the outcome was unaffected by which one was moving. This was one of the principal paths that led him vĩ đại develop special relativity.^{[24]}

## Applications

The principles of electromagnetic induction are applied in many devices and systems, including:

### Electrical generator

The emf generated by Faraday's law of induction due vĩ đại relative movement of a circuit and a magnetic field is the phenomenon underlying electrical generators. When a permanent magnet is moved relative vĩ đại a conductor, or vice versa, an electromotive force is created. If the wire is connected through an electrical load, current will flow, and thus electrical energy is generated, converting the mechanical energy of motion vĩ đại electrical energy. For example, the *drum generator* is based upon the figure vĩ đại the bottom-right. A different implementation of this idea is the Faraday's disc, shown in simplified khuông on the right.

In the Faraday's disc example, the disc is rotated in a uniform magnetic field perpendicular vĩ đại the disc, causing a current vĩ đại flow in the radial arm due vĩ đại the Lorentz force. Mechanical work is necessary vĩ đại drive this current. When the generated current flows through the conducting rim, a magnetic field is generated by this current through Ampère's circuital law (labelled "induced B" in the figure). The rim thus becomes an electromagnet that resists rotation of the disc (an example of Lenz's law). On the far side of the figure, the return current flows from the rotating arm through the far side of the rim vĩ đại the bottom brush. The B-field induced by this return current opposes the applied B-field, tending vĩ đại *decrease* the flux through that side of the circuit, opposing the *increase* in flux due vĩ đại rotation. On the near side of the figure, the return current flows from the rotating arm through the near side of the rim vĩ đại the bottom brush. The induced B-field *increases* the flux on this side of the circuit, opposing the *decrease* in flux due vĩ đại r the rotation. The energy required vĩ đại keep the disc moving, despite this reactive force, is exactly equal vĩ đại the electrical energy generated (plus energy wasted due vĩ đại friction, Joule heating, and other inefficiencies). This behavior is common vĩ đại all generators converting mechanical energy vĩ đại electrical energy.

### Electrical transformer

When the electric current in a loop of wire changes, the changing current creates a changing magnetic field. A second wire in reach of this magnetic field will experience this change in magnetic field as a change in its coupled magnetic flux, . Therefore, an electromotive force is mix up in the second loop called the induced emf or transformer emf. If the two ends of this loop are connected through an electrical load, current will flow.

#### 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 vĩ đại either measure the current in it or, in reverse, vĩ đại induce a voltage. Unlike conventional instruments the clamp does not make electrical liên hệ with the conductor or require it vĩ đại be disconnected during attachment of the clamp.

### 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 ε generated in the magnetic field *B* due vĩ đại a conductive liquid moving at velocity *v* is thus given by:

where ℓ is the distance between electrodes in the magnetic flow meter.

## Eddy currents

Electrical conductors moving through a steady magnetic field, or stationary conductors within a changing magnetic field, will have circular currents induced within them by induction, called eddy currents. Eddy currents flow in closed loops in planes perpendicular vĩ đại the magnetic field. They have useful applications in eddy current brakes and induction heating systems. However eddy currents induced in the metal magnetic cores of transformers and AC motors and generators are undesirable since they dissipate energy (called core losses) as heat in the resistance of the metal. Cores for these devices use a number of methods vĩ đại reduce eddy currents:

- Cores of low frequency alternating current electromagnets and transformers, instead of being solid metal, are often made of stacks of metal sheets, called
*laminations*, separated by nonconductive coatings. These thin plates reduce the undesirable parasitic eddy currents, as described below. - Inductors and transformers used at higher frequencies often have magnetic cores made of nonconductive magnetic materials such as ferrite or iron powder held together with a resin binder.

### Electromagnet laminations

Eddy currents occur when a solid metallic mass is rotated in a magnetic field, because the outer portion of the metal cuts more magnetic lines of force kêu ca the inner portion; hence the induced electromotive force is not uniform; this tends vĩ đại cause electric 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, sánh as vĩ đại show the subdivision of the eddy currents. In practical use, the number of laminations or punchings ranges from 40 vĩ đại 66 per inch (16 vĩ đại 26 per centimetre), and brings the eddy current loss down vĩ đại about one percent. While the plates can be separated by insulation, the voltage is sánh low that the natural rust/oxide coating of the plates is enough vĩ đại prevent current flow across the laminations.^{[25]}

Xem thêm: để 2 vecto cùng phương

This is a rotor approximately 20 mm in diameter from a DC motor used in a CD player. Note the laminations of the electromagnet pole pieces, used vĩ đại limit parasitic inductive losses.

### Parasitic induction within conductors

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 vĩ đại break up the eddy flows that can khuông within large solid conductors. The same principle is applied vĩ đại transformers used at higher kêu ca power frequency, for example, those used in switch-mode power supplies and the intermediate frequency coupling transformers of radio receivers.

## See also

- Alternator
- Crosstalk
- Faraday paradox
- Hall effect
- Inductance
- Moving magnet and conductor problem

## References

### Notes

**^**The EMF is the voltage that would be measured by cutting the wire vĩ đại create an open circuit, and attaching a voltmeter vĩ đại the leads. Mathematically, 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).*Magnetism and Electricity: A Manual for Students in Advanced Classes*. London and New York: Longmans, Green, & Co. p. 285.- ^
^{a}^{b}Giancoli, Douglas C. (1998).*Physics: Principles with Applications*(5th ed.). pp. 623–624. **^**Ulaby, Fawwaz (2007).*Fundamentals of applied electromagnetics*(5th ed.). Pearson: Prentice Hall. p. 255. ISBN 978-0-13-241326-8.**^**"Joseph Henry".*Distinguished Members Gallery, National Academy of Sciences*. Archived from the original on 2013-12-13. Retrieved 2006-11-30.**^**Errede, Steven (2007). "A Brief History of The Development of Classical Electrodynamics" (PDF).**^**"Electromagnetism".*Smithsonian Institution Archives*.**^***Michael Faraday*, by L. Pearce Williams, pp. 182–183**^***Michael Faraday*, by L. Pearce Williams, pp. 191–195- ^
^{a}^{b}*Michael Faraday*, by L. Pearce Williams, p. 510 **^**Maxwell, James Clerk (1904),*A Treatise on Electricity and Magnetism*, Vol. II, Third Edition. Oxford University Press, pp. 178–179 and 189.**^**"Archives Biographies: Michael Faraday", The Institution of Engineering and Technology.**^**Good, R. H. (1999).*Classical Electromagnetism*. Saunders College Publishing. p. 107. ISBN 0-03-022353-9.**^**Feynman, R. Phường.; Leighton, R. B.; Sands, M. L. (2006).*The Feynman Lectures on Physics, Volume 2*. Pearson/Addison-Wesley. p. 17-2. ISBN 0-8053-9049-9.**^**Griffiths, D. J. (1999).*Introduction vĩ đại Electrodynamics*(3rd ed.). Prentice Hall. pp. 301–303. ISBN 0-13-805326-X.**^**Tipler, Phường. A.; Mosca, G. (2003).*Physics for Scientists and Engineers*(5th ed.). W.H. Freeman. p. 795. ISBN 978-0716708100.**^**Jordan, E.; Balmain, K. G. (1968).*Electromagnetic Waves and Radiating Systems*(2nd ed.). Prentice-Hall. p. 100. ISBN 978-0132499958.**^**Hayt, W. (1989).*Engineering Electromagnetics*(5th ed.). McGraw-Hill. p. 312. ISBN 0-07-027406-1.**^**Schmitt, R. (2002).*Electromagnetics Explained*. Newnes. p. 75. ISBN 978-0750674034.**^**Whelan, Phường. M.; Hodgeson, M. J. (1978).*Essential Principles of Physics*(2nd ed.). John Murray. ISBN 0-7195-3382-1.**^**Nave, C. R. "Faraday's Law".*HyperPhysics*. Georgia State University. Retrieved 2011-08-29.**^**Maxwell, J. C. (1861). "On physical lines of force".*Philosophical Magazine*.**90**(139): 11–23. doi:10.1080/14786446108643033.**^**Griffiths, D. J. (1999).*Introduction vĩ đại Electrodynamics*(3rd ed.). Prentice Hall. pp. 301–303. ISBN 0-13-805326-X. Note that the law relating flux vĩ đại EMF, which this article calls "Faraday's law", is referred vĩ đại by Griffiths as the "universal flux rule". He uses the term "Faraday's law" vĩ đại refer vĩ đại what this article calls the "Maxwell–Faraday equation".**^**"The flux rule" is the terminology that Feynman uses vĩ đại refer vĩ đại the law relating magnetic flux vĩ đại EMF. Feynman, R. Phường.; Leighton, R. B.; Sands, M. L. (2006).*The Feynman Lectures on Physics, Volume II*. Pearson/Addison-Wesley. p. 17-2. ISBN 0-8053-9049-9.**^**Einstein, A. (1905). "Zur Elektrodynamik bewegter Körper" (PDF).*Annalen der Physik*.**17**(10): 891–921. Bibcode:1905AnP...322..891E. doi:10.1002/andp.19053221004.

- 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.

- Translated in Einstein, A. (1923). "On the Electrodynamics of Moving Bodies" (PDF).
- ^
^{a}^{b}^{c}Images and reference text are from the public domain name 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

- 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

- Media related vĩ đại Electromagnetic induction at Wikimedia Commons
- Tankersley and Mosca:
*Introducing Faraday's law* - A không lấy phí java simulation on motional EMF

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