A parallel-plate capacitor is being charged

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electric current and circuits · Electric current and circuits

Electricity, Magnetism and Electromagnetism, Ch Current, current density, conductivity and Ohm's law

Problem

A parallel-plate capacitor is being charged. The lead to plate A carries a steady current of

3.5\,\mathrm{A}

towards plate A, and the lead from plate B carries a steady current of

3.5\,\mathrm{A}

away from plate B. No charge crosses the gap between the plates. A student draws a closed surface

S

, with the outward normal, that encloses the whole capacitor (both plates and the gap) and cuts through both leads, and argues: "Charge is being pushed in on one side and pulled off on the other, and both processes add charge to the region, so

3.5 + 3.5 = 7.0

and the charge enclosed by

S

grows at

7.0\,\mathrm{C\,s^{-1}}

." ((a)) State the error in the argument, and give the correct value of

dQ_{\mathrm{enc}}/dt

for the surface

S

. ((b)) Give

dQ/dt

for a closed surface that encloses plate A alone (again with the outward normal), cutting only its lead.

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