Question

A parallel plate capacitor with circular plates of radius $R$ is being charged as shown. At the instant shown, the displacement current in the region between the plates enclosed between $\frac{R}{2}$ and $R$ is given by

• A. $\frac{4}{3}i$
• B. $\frac{1}{4}i$
• C. $3i$
• D. $\frac{3}{4}i$

Answer 1

Answer: (B)

Displacement current is given by

$I={\epsilon }_0\frac{d{\varphi }_e}{dt}$

$={\epsilon }_{0}A\frac{dE}{dt}(\because \varphi =A.E)$

$=A\frac{d}{dt}\left(\frac{q}{A^{{}^{\prime }}}\right)$

$=\frac{A}{A^{{}^{\prime }}}i(\because \frac{dq}{dt}=i)$

$=\frac{\pi {\left(\frac{R}{2}\right)}^2}{\pi R^2}$

$=\frac{1}{4}i$