Question

A single circular loop of wire of radius r = 2.5cm rotates at a frequency of 60 Hz in a constant magnetic field of magnitude B = 1.8 T.
Use this to design a generator that produces an induced emf of 430 V. Hint: You must choose values for the number of loops and the area of each loop.

number of loops = ?
area of a loop = ?

I don't even know where to start ... My professor did not cover this material yet & our textbook does not go over generators.

Answer 1

It is a loop of wire operating in a changing magnetic field, changing because sometimes the B flux is through the plane of the coil and sometimes it is parallel to the plane of the coil and no B goes through the coil.
B = 1.8 Tesla
B through coil = 1.8 sin 2 pi f t
f = 60
so 2 pi f = 377
so
B for us = 1.8 sin 377 t
dB/dt = 1.8*377 cos 377 t
area = pi r^2 = pi (.025)^2 = .00196 m^2
(answer to part B by the way)
so
d flux/dt = .00196*1.8*377 cos 377 t
= 1.33 cos 377 t
he voltage in a single loop is then
EMF = -d flux/dt
= 1.33 cos 377 t
so to get 430 volts we need
430/1.33 = 323 loops



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