A loop of wire of radius a = 45 mm has an electrical resistance R = 0.038 . The

Question

A loop of wire of radius a = 45 mm has an electrical resistance R = 0.038 . The loop is initially inside a uniform magnetic field of magnitude B0 = 1.6 T parallel to the loop's axis. The magnetic field is then reduced slowly at a constant rate, which induces a current I = 0.20 A in the loop. How long does it take for the magnitude of the uniform magnetic field to drop from 1.6 T to zero?

Find the time t it takes the magnetic field to drop to zero.

Express your answer in seconds using two significant figures.

Explanation / Answer

The magnetic flux phi = N B A cos @
Here @ = 0, A = pi *(0.045)^2, N = 1
Now induced emf = - d(phi)/dt = I * R = 0.2*0.038 = - 0.0076 V
So e = A * dB/dt
dB = 0 - 1.6 = -1.6 T
Plugging we get dt = pi (0.045)^2 *1.6/ 0.0076 = 1.34 s

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