N circular loops of copper wire rotate in a uniform magnetic field B. The radius

Question

N circular loops of copper wire rotate in a uniform magnetic field B. The radius of the loops is given by R and the period of rotation by T. (a) Derive a formula for the EMF generated in the wire as a function of time, (b) Calculate the electric field along the loops of wire given that there are 15 loops of wire, the magnetic field is 2.50 Tesla, the diameter of the loops is 12.0 cm, and the rotational speed is 4000 rpm. (c) If the total resistance of the loops of wire is 0.250 ohms, what will be the rms current in the wire?

Explanation / Answer

Here ,

a) for the emf generated as a function of time

EMF = N * B *pi * R^2 *(2pi/T) sin(2pi * t/T)

EMF = N* B * 2pi^2*R^2/T * sin(2pi *t/T)

b)

w = 4000 rpm = 418.8 rad/s

EMF = 15 * 2.50 * pi * (0.12/2)^2 * (418.8)

EMF = 177.6 V

electric field = 177.6/(2pi * 0.12/2 * 15)

electric field = 31.4 V/m

c)

rms current = 177.6/(0.250 * sqrt(2))
rms current = 502 A

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