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 is
`E=(q)/(Aepsilon_(0))=(It)/(Aepsilon_(0))" …(i)"`
Electric flux through the givne are A/2 is
`phi_(E)=((A)/(2))E=(It)/(2epsilon_(0))" (Using (i)) ...(ii)"`
The refore, displacement current `I_(d)=epsilon_(0)(dphi_(E))/(dt)`
`=epsilon_(0)(d)/(dt)((It)/(2epsilon_(0)))=(I)/(2)" (Using (ii))"`