# Electrical Generator and rotating coil

1. Feb 19, 2013

### SereneKi

1. The problem statement, all variables and given/known data

An electric generator consists of a rectangular coil of wire rotating about its longitudinal axis which is perpendicular to a magnetic field of B = 1.70 × 10-2 T. The coil measures 13.00 cm by 19.00 cm and 200.00 turns of wire. The ends of the wire are connected to an external circuit. At what speed must you rotate this coil in order to induce an alternating emf of amplitude 11.00 V between the ends of the wire? Give you answer in rev/s. Do not enter the units.

2. Relevant equations

Eind=-N d(BAcos(theta))/ dt

3. The attempt at a solution

I know that because this has a turning coil in a magnetic field, the above equation can become Eo=-NBA

and thus Eo=0.08398 V

I just don't know where to go form here or how you are supposed to find the speed?

2. Feb 19, 2013

### TSny

You'll need to express θ as a function of time so that you can carry out the time derivative in your expression.

3. Feb 19, 2013

### SereneKi

Eind=-NBA*dcos(theta)/dt

is that what you meant?

4. Feb 19, 2013

### TSny

You can assume that the generator is rotating at constant angular speed ω. So, θ = ωt.
Using that, can you evaluate d(cosθ)/dt?

5. Feb 19, 2013

### SereneKi

d(cos(wt))/dt

θ=2(pi)ft = wt

emf=NBAw

is that right?

6. Feb 19, 2013

### TSny

Looks good to me.

7. Feb 19, 2013

### SereneKi

so w= 11/ 200 * 1.7*10^-2 * .13 * .19

w=130.99

What now, Lon capa says that isn't the answer

8. Feb 19, 2013

### TSny

What are the units of w in emf= NBAw?

Note that you are asked to find the rotation rate in rev/s.

9. Feb 19, 2013

### SereneKi

They are rad/s! So 130.99 / 2pi = 20.85 which is right! thank you so much!