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 $\frac{A}{2}$ parallel to the plate and down symmetrically between the plates. Find the displacement current through this area.

• A. $i_d=\frac{i}{8}$
• B. $i_d=\frac{i}{2}$
• C. $i_d=\frac{i}{3}$
• D. $i_d=\frac{i}{4}$

Answer 1

The correct option is B $i_d=\frac{i}{2}$

Displacement current $=\frac{dQ}{dt}=\frac{d\left(CV\right)}{dt}$

$=C\frac{dV}{dt}=C(d.\frac{dE}{dt})$

$=\frac{A{ϵ}_0}{d}.d\frac{dE}{dt}$

$=A{ϵ}_0\frac{dE}{dt}\propto A$

Hence, current halves when area of plates halves.