Question

A parallel-plate capacitor with plate area A and separation between the plates d, is charged by a constant current i. Consider a plane surface of area A/2 parallel to the plates and drawn symmetrically between the plates. Find the displacement current through this area.

• A. i
• B. $\frac{i}{2}$
• C. $\frac{i}{3}$
• D. $\frac{i}{4}$

Answer 1

The correct option is B

$\frac{i}{2}$

Suppose the charge on the capacitor at time t is Q. The electric field between the plates of the capacitor is E = $\frac{Q}{{ϵ}_{0}A}$. The flux through the area considered is ${\varphi }_E=\frac{Q}{{ϵ}_{0}A}.\frac{A}{2}=\frac{Q}{2{ϵ}_0}.$
The displacement current is
$i_d={ϵ}_0\frac{d{\varphi }_E}{dt}={ϵ}_0\left(\frac{1}{2{ϵ}_0}\right)\frac{dQ}{dt}=\frac{i}{2}.$