A circular coil enclosing an area of 200 cm2 is made of 210 turns of copper wire

Question

A circular coil enclosing an area of 200 cm2 is made of 210 turns of copper wire. The wire making up the coil has resistance of 7.0 , and the ends of the wire are connected to form a closed circuit. Initially, a 1.6-T uniform magnetic field points perpendicularly upward through the plane of the coil. The direction of the field then reverses so that the final magnetic field has a magnitude of 1.6 T and points downward through the coil. If the time required for the field to reverse directions is 0.40 s, what is the average current (in Amps) in the coil during that time?

Explanation / Answer

Given

N = 210

A = 200 cm^2 = 0.02 m^2

resistance R = 7 ohm

initial field B1 = 1.6 T

final field B2 = -1.6 T

dt = 0.4 s

induced emf e = N * dphi/dt

e = N * A * dB/dt

e = 210 * 0.02 * (1.6 - (-1.6))/0.4

e = 33.6 V

average current I = e/R

I = 33.6/7

I = 4.8 A

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