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Three identical conducting circular loops, A, B and C, are placed in magnetic fields. In each loop the interior is split by a diameter (dashed line) into two regions, each containing a magnetic field that is either increasing (INCR) or decreasing (DECR) in magnitude at the same rate. Comparing the magnitudes of the induced currents I_A, I_B and I_C, which relation is correct?

1. I_A > I_B = I_C
2. I_A = I_C > I_B
3. I_A = I_B = I_C
4. I_C > I_A > I_B

Correct answer: I_A = I_C > I_B

Solution

The induced emf is governed by the net dC(flux)/dt summed over both half-regions. When the two halves contribute changes that reinforce (both add to the net flux change), the emf and current are large; when they oppose, the net change is small. Two of the loops (here A and C) give reinforcing contributions and hence equal, larger currents, while the third (B) gives a smaller net change. Thus I_A = I_C > I_B.

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