A parallel plate capacitor has circular plates, each of radius `5.0 cm.` It is being charged so that electric field in the gap between its plates rises steadily at the rate of `10^(12) "Vm"^(-1)"s"^(-1).`What is the displacement current?

Options

A. `0.14 A`
B. `0.21 A`
C. `0.28 A`
D. `0.35 A`

Answer

C

Explanation

`r = 10 cm = 10^(-1) m and (dE)/(dt) = 10^(12)V//m//s`
`:. A = pi r^(2) = pi(10^(-2))`
The displacement current, `I_(D) = epsilon_(0)(d phi_(E))/(dt) but phi_(E) = E xx A`
`:. I_(D) = epsilon_(0)A (dE)/(dt) = epsilon_(0) xx pir^(2) xx (dE)/(dt)`
`=8.85 xx 10^(-12) xx 3.14 xx 10^(-2) xx 10^(12)`
`=27.78 xx 10^(-2) = 0.2778`
`I_(D) -: 0.28 A`.