Electromagnetic induction is where a current is produced in a conductor through a changing magnetic flux.

Magnetic flux

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Magnetic flux is the strength of the magnetic field going through an area. It is the product of the magnetic field (B), the area (A) that it is going through and the angle (a) between the line 90 degrees to the area and the magnetic field lines. Magnetic flux is represented by the symbol $\{\backslash Phi\}$, therefore we can say that $\{\backslash Phi\}$ = BAcos(a) and the resulting unit will be $Tm^2$, where T is the unit for magnetic field and $m^2$ is the unit for area.

The changing magnetic flux generates an electromotive force (EMF). This force then pushes free electrons in a certain way, which in turn creates a current.

Faraday's Law

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

His laws states that:

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

where,

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

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

$dt$ is the change in time, measured in seconds.

In the case of a solenoid:

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

where,

N is the number of loops in the solenoid.

Lenz's Law

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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.

Mathematics | Physics | Electromagnetic induction