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Two concentric, coplanar circular coils have radii a and b with b >> a. The resistance of the inner coil is R. The current in the outer coil is raised steadily from 0 to i. Find the total charge that circulates through the inner coil.

1. mu0 pi a² i / (2 b R)
2. mu0 pi a² i / (b R)
3. mu0 a² i / (2 b R)
4. mu0 pi b² i / (2 a R)

Correct answer: mu0 pi a² i / (2 b R)

Solution

The outer coil produces a nearly uniform field mu0 i/(2 b) over the small inner coil, giving flux Phi = mu0 i pi a²/(2 b). The induced charge is q = delta Phi / R = mu0 pi a² i/(2 b R).

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