H2 Physics 18 - Electromagnetic Induction: E.M.F. in a Rotating Coil

Step 1 - State the problem

A rectangular coil has one hundred and twenty turns, each of area forty square centimetres.

Step 1 - State the problem

The coil rotates at fifty revolutions per second in a uniform magnetic field of zero point one five tesla.

Step 1 - State the problem

We want to find the peak e.m.f. induced in the coil.

Step 2 - Write the expression for magnetic flux and induced e.m.f.

The magnetic flux through the coil is Phi equals B A cosine omega t, where omega is the angular frequency.

Step 2 - Write the expression for magnetic flux and induced e.m.f.

By Faraday's law, the induced e.m.f. equals minus N times the rate of change of flux.

Step 2 - Write the expression for magnetic flux and induced e.m.f.

Differentiating gives e equals N B A omega sine omega t.

Step 3 - Calculate the angular frequency

The angular frequency omega equals two pi f.

Step 3 - Calculate the angular frequency

Substituting: omega equals two pi times fifty, which gives one hundred pi, or approximately three hundred and fourteen radians per second.

Step 4 - Find the peak e.m.f.

The peak e.m.f. E nought equals N B A omega.

Step 4 - Find the peak e.m.f.

Substituting: E nought equals one hundred and twenty times zero point one five times four point zero times ten to the minus three times one hundred pi.

Step 4 - Find the peak e.m.f.

First, one hundred and twenty times zero point one five is eighteen.

Step 4 - Find the peak e.m.f.

Then eighteen times four point zero times ten to the minus three is zero point zero seven two.

Step 4 - Find the peak e.m.f.

Finally, zero point zero seven two times one hundred pi gives approximately twenty-two point six volts.

Step 5 - Find the r.m.s. e.m.f. and state key points

For a sinusoidal e.m.f., the r.m.s. value is the peak divided by root two.

Step 5 - Find the r.m.s. e.m.f. and state key points

E r.m.s. equals twenty-two point six divided by root two, which gives approximately sixteen point zero volts.

Step 5 - Find the r.m.s. e.m.f. and state key points

Remember: Lenz's law tells us the direction of the induced e.m.f. always opposes the change in flux that produced it.

Step 5 - Find the r.m.s. e.m.f. and state key points

This is why there is a minus sign in Faraday's law. In calculations, we usually just find the magnitude.