7.5.6

# Electromagnetic Induction 2

Test yourself

## Producing A.C. Using Induction

A coil can be rotated in a magnetic field to produce alternating current (a.c).

### Experimental set up

• Faraday’s law says that the induced emf is directly proportional to the rate of change of flux linkage.
• The flux linkage through the coil is BAN cosθ.
• For this coil, θ = ωt, where ω = 2πf and f is the frequency of rotation.
• Thus the flux linkage is BAN cos(ωt) and the emf will be directly proportional to BANω sin(ωt).
• Finally, if f is increased, this not only increases the frequency of induced emf, it also increases the amplitude of the induced emf.

## Induced Electromotive Force

When a coil is rotating in a magnetic field, the flux linkage is constantly changing. This induces an electromotive force (emf).

### A rotating coil

• A coil is made of N turns and has an area A and is rotating at an angular velocity ${\omega}$.
• If the coil rotates, it 'cuts' the field lines. This induces an emf.

### Calculation

• The equation for the emf induced is:
• Emf induced = field strength x area x number of coils x angular speed x $sin({\omega}t)$
• $emf=BAN{\omega}sin({\omega}t)$