Question

A parallel plate condenser has two circular metal plates of radius 15 cm. It is being charged so that electric field in the gap between its plates rises steadily at the rate of ${10}^{1}2V/ms.$ what is the displacement current?

• A. 0.07$A$
• B. 1.39$A$
• C. 13.9$A$
• D. 139$A$

Answer 1

Answer: (A)

0.07$A$

$\begin{array}{c}Id={\in }_0\frac{d\varphi }{dt}={\in }_0\frac{d\left(EA\right)}{dt}={\in }_{0}A\frac{EA}{dt}=\in \frac{\pi r^{2}dE}{dt}\\ =8.85\times {10}^{-12}\times 3.14\times 25\times {10}^{-4}\times {10}^{12}\\ =0.07A\end{array}$

Hence,

option $\left(A\right)$ is correct answer.