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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Electromagnetic induction | 1/3 | https://en.wikipedia.org/wiki/Electromagnetic_induction | reference | science, encyclopedia | 2026-05-05T10:55:06.297489+00:00 | kb-cron |
Electromagnetic induction 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 to 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. It was discovered independently by Joseph Henry in 1832. In Faraday's first experimental demonstration, on August 29, 1831, he wrapped two wires around opposite sides of an iron ring or "torus" (an arrangement similar to a modern toroidal transformer). Based on his understanding of electromagnets, he expected that, when current started to 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 to a battery. He saw a transient current, which he called a "wave of electricity", when he connected the wire to the battery and another when he disconnected it. This induction was due to the change in magnetic flux that occurred when the battery was connected and disconnected. 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"). 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. An exception was James Clerk Maxwell, who used Faraday's ideas as the basis of his quantitative electromagnetic theory. In Maxwell's model, the time varying aspect of electromagnetic induction is expressed as a differential equation, which Oliver Heaviside referred to 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 form recognized today in the group of equations known as Maxwell's equations. In 1834 Heinrich Lenz formulated the law named after him to 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 ΦB through a region of space enclosed by a wire loop. The magnetic flux is defined by a surface integral:
Φ
B
=
∫
Σ
B
⋅
d
A
,
{\displaystyle \Phi _{\mathrm {B} }=\int _{\Sigma }\mathbf {B} \cdot d\mathbf {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 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). 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:
E
=
−
d
Φ
B
d
t
,
{\displaystyle {\mathcal {E}}=-{\frac {d\Phi _{\mathrm {B} }}{dt}}\,,}
where
E
{\displaystyle {\mathcal {E}}}
is the emf and ΦB 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. This is due to the negative sign in the previous equation. To increase the generated emf, a common approach is to 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.
E
=
−
N
d
Φ
B
d
t
{\displaystyle {\mathcal {E}}=-N{\frac {d\Phi _{\mathrm {B} }}{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 ===
In general, the relation between the emf
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 _{\Sigma }\mathbf {B} \cdot d\mathbf {A} \,,}
the integral form of the Maxwell–Faraday equation can be written as:
∮
∂
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 d\mathbf {A} }\,.}
It is one of the four Maxwell's equations, and therefore plays a fundamental role in the theory of classical electromagnetism.