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. `i//8`

Answer

b

Explanation

Charge on capacitor plates at time `t is, q = it` Electric field between the plates at this instant.
`E=(q)/(Aepsilon_(0))=(it)/(Aepsilon_(0))`
Electric flux through the given area
`phi_(E)=((A)/(2))E=(it)/(2epsilon_(0))`
Therefore, displacement current
`i_(d)=epsilon_(0)(dphi_(E))/(dt)`
`epsilon_(0)(d)/(dt) ((it)/(2epsilon_(0)))=(i)/(2)`