# Electromagnetic induction

production of voltage by a varying magnetic field

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.

## 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.

## Lenz's law

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.