Electromagnetic induction

Electromagnetism
Electricity · Magnetism · Magnetic permeability
Electrostatics Electric charge • Coulomb's law • Electric field • Electric flux • Gauss's law • Electric potential energy • Electric potential • Electrostatic induction • Electric dipole moment • Polarization density
Magnetostatics Ampère's law • Electric current • Magnetic field • Magnetization • Magnetic flux • Biot–Savart law • Magnetic dipole moment • Gauss's law for magnetism
Electrodynamics Lorentz force law • emf • Electromagnetic induction • Faraday’s law • Lenz's law • Displacement current • Maxwell's equations • EM field • Electromagnetic radiation • Liénard–Wiechert potential • Maxwell tensor • Eddy current
Electrical Network Electrical conduction • Electrical resistance • Capacitance • Inductance • Impedance • Resonant cavities • Waveguides
Covariant formulation Electromagnetic tensor • EM Stress-energy tensor • Four-current • Electromagnetic four-potential
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Electromagnetic induction is where a voltage or current is produced in a conductor by a changing magnetic flux. It may happen when a magnet is moved in a solenoid, or when a solenoid is constantly moved in a stationary magnetic field, thus changing the magnetic flux.

When a coiled wire is introduced near a magnet, the magnetic lines of force pass through the coil. This causes the magnetic flux to change. Magnetic flux is represented by the symbol ${\displaystyle {\Phi }}$, therefore we can say that ${\displaystyle {\Phi }}$ = BAcos(a) and the resulting unit will be ${\displaystyle Tm^{2}}$, where T is the unit for magnetic field and ${\displaystyle m^{2}}$ is the unit for area.

The changing magnetic flux generates an electromotive force (EMF). This force moves free electrons in a certain way, which constitute a current.

Michael Faraday found that an electromotive force is generated when there is a change in magnetic flux in a conductor.

His laws state that:

${\displaystyle {\mathcal {E}}={-{d\Phi } \over dt}}$

where,

${\displaystyle {\mathcal {E}}}$ is the electromotive force, measured in volts;

${\displaystyle {d\Phi }}$ is the change in magnetic flux, measured in webers;

${\displaystyle dt}$ is the change in time, measured in seconds.

In the case of a solenoid:

${\displaystyle {\mathcal {E}}={-N{d\Phi } \over dt}}$

where,

N is the number of loops in the solenoid.

The negative sign in both equation above is a result of Lenz's law, named after Heinrich Lenz. His law states that the electromotive force (EMF) produces a current that opposes the motion of the changing magnetic flux.

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