One plate of a capacitor is charged through a single connecting wire

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

One plate of a capacitor is charged through a single connecting wire. A steady current of

3.0\,\mathrm{A}

flows along the wire into the plate, and no current leaves the plate anywhere else (the gap between the plates is a vacuum and carries no charge across it). Imagine a closed surface

S

that encloses the whole plate and cuts the connecting wire once; the outward normal is taken on

S

as usual. The plate carries no charge at

t = 0

. ((a)) What is the outward flux

\oint_S \mathbf{J}\cdot d\mathbf{A}

? ((b)) At what rate does the charge enclosed by

S

change? ((c)) How much charge is on the plate after

4.0\,\mathrm{ms}

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