Question

A parallel plate capacitor consists of circular plates with radius $10cm$ , separated by a distance of $0.5mm$. The capacitor is charged by an external source such that the electric field between the plates changes at a rate $5\times {10}^{13}Vm-1s-1$. The displacement current through the capacitor is

• A. $1.4mA$
• B. $14mA$
• C. $14A$
• D. $1.4A$

Answer 1

Answer: (C)

$14A$

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

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

$=\frac{A{ϵ}_0}{d}.d\frac{dE}{dt}$

$=A{ϵ}_0\frac{dE}{dt}$

$=\pi r^2{ϵ}_0\frac{dE}{dt}$

$=14A$