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A capacitor with circular parallel plates of radius R = 1.20 cm is being discharged by a 12.0 A current. The largest induced magnetic field in the gap has magnitude 12.0 mT (this occurs at the plate edge, r = R). At which radius b is the induced magnetic field magnitude 3.00 mT inside the gap (i.e. for r < R)?

1. 0.3 cm
2. 2.7 cm
3. 4.8 cm
4. 5.4 cm

Correct answer: 0.3 cm

Solution

Inside the capacitor gap the displacement current is uniformly distributed, so B is proportional to r and is maximum at r = R (= 12.0 mT). For B = 3.00 mT inside, b = R*(B/B_max) = 1.20*(3.00/12.0) = 0.30 cm.

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