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Question

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 symmetrically between the plates. Find the displacement current through this area.


A

i

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B

i2

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C

i3

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D

i4

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Solution

The correct option is B

i2


Suppose the charge on the capacitor at time t is Q. The electric field between the plates of the capacitor is E = Qϵ0A. The flux through the area considered is ϕE=Qϵ0A.A2=Q2ϵ0.
The displacement current is
id=ϵ0dϕEdt=ϵ0(12ϵ0)dQdt=i2.


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