Question

A parallel plate capacitor with plate are A and separation between the plates $d$ is charged by a current $i$ . Displacement current through a plane surface of area $A/2$ parallel to the plates and draw symmetrically between the plates is:

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

Answer 1

The correct option is B $\frac{i}{4}$

Given, $Area=A,distance=dcurrent=i$

If $q$ be the charge on the capacitor at time $t_1$, then the electric field between the plates of the capacitors is:

$E=\frac{q}{{\epsilon }_{0}A}$

Flux through the area $\varphi E=\left(\frac{q}{{\epsilon }_{0}A}\right)\left(\frac{A}{4}\right)=\frac{q}{4{\epsilon }_0}$

Displacement current $I_D=E_0=\frac{d\varphi E}{dt}=\frac{d\left(\frac{q}{4}\right){\epsilon }_0}{dt}=\frac{1}{4}\frac{dq}{dt}=\frac{i}{4}$