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A parallel-plate capacitor with square plates of side L is being discharged by a current of 0.75 A. Viewing one plate head-on from inside the capacitor, consider a dashed rectangular Amperian loop of width W and height H lying in the gap. With L = 12 cm, W = 4.0 cm and H = 2.0 cm, evaluate the line integral of B around the dashed rectangle (the circulation of B over the loop).

1. 5.2e-8 T*m
2. 1.0e-7 T*m
3. 2.1e-7 T*m
4. 3.3e-7 T*m

Correct answer: 5.2e-8 T*m

Solution

Between the plates the displacement current density is uniform, so the displacement current through the loop equals the total current times the fraction of plate area enclosed: I_enc = I*(W*H)/L² = 0.75 * (0.04*0.02)/(0.12²) = 0.75 * 0.0008/0.0144 = 0.75 * 0.05556 = 0.04167 A. By the Ampere-Maxwell law, the circulation of B = mu0 * I_enc = (4*pi e-7) * 0.04167 ~= 5.24e-8 T*m.

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