# 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, thus changing the magnetic flux.

If the magnet is stationary, there will be no produced voltage (electrostatic potential difference) across an electrical conductor. However, if the magnetic field is changing and (maintaining) movement, while continuously directing in the opposite direction (varying its direction periodically), it will cause a the production of a voltage (hence the flow of alternating current), as stated by Michael Faraday in 1831.

## 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.