A solenoid has a magnetic field of 1 Tesla, has a current of 10 amps , has 39,78

Question

A solenoid has a magnetic field of 1 Tesla, has a current of 10 amps , has 39,789 turns and the length of the wire is .5 m. To measure the magnetic field in the solenoid you build a small coil from 10 turns of wire in a 1.18 inch or 3 cm diameter loop. If you spin the loop (along the axis of the diameter) at 100 RPM in the magnetic field, what would you expect to measure for an induced electromotive force if the solenoid is at full field of 1 Tesla.

Please could you explain the answer in detail and in step by step form and explain any equations that you used and where you got them from or how you derived the equation as I want to understand the solution. I would greatly appreciate your help as I really need this. Thank You.

Explanation / Answer

Magnetic Flux through one turn = B.A

In this case B.A = BA.

So, total flux through coil = NBA.

emf = -d(Flux)/dt

Since the rotation is at a constant rate of 100 RPM or 100/60 Hz,

emf = NBAf = 0.0118 V

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