A parallel- plate capacitor with plate area A and separation between the plates d, is charged by a constant current i. Consider a plane surface of area A/2 parallel to the plates and drawn summetrically between the plates. Find the displacement current through this area.

Options

A. `i`
B. `(i)/(2)`
C. `(i)/(4)`
D. None of these

Answer

b

Explanation

Suppose the charge on the capacitor at time `t` is `Q`, the electric field between the plates of the capacitor is `E=(Q)/(epsilon_(0)A)`. The flux through the area considered is
`phi_(E)=(Q)/(epsilon_(0)A).(A)/(2)=(Q)/(2epsilon_(0))`
`:.` The displacement current
`i_(d)=epsilon_(0)(dphi_(E))/(dt)=epsilon_(0)((1)/(2epsilon_(0)))(dQ)/(dt)=(i)/(2)`.