This question should be fairly easy once we have done Lecture 20

This tutorial should help you get use to applying Faraday's law to a loop in a magnetic field.

Another tutorial on Faraday's Law. For Part F refer to the notes on the electric field produced by a time varying magnetic field.

Most of the examples we looked at in class concerned flux changing either because the field changed or a loop turned, but the flux can also change if the size of a loop is changed, and then $\frac{d\Phi_{B}}{dt}=B\frac{dA}{dt}=-\mathcal{E}$

Apply the formula for the emf produced by a generator.

The discussion we had about the mutual inductance of a solenoid and a coil may help you here.

You can think of the back emf in the motor as being similar to the emf produced by a generator.

The magnetic field goes from one extreme to another **twice** every shake, once you have worked out $\frac{dB}{dT}$ use

$\mathcal{E}=-\frac{dB}{dT}NA$

to work out what $N$ should be.