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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.

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Solution

Given that,

Area A=A2

Separation between the plates =d

Constant current =i

Now, the electric field between plates of the capacitor

E=qε0A

Now, the flux through the area

ϕE=qε0A×A2

ϕE=q2ε0

Now, the displacement current is

Id=ε0×dϕEdt

Id=ε0×d(q2ε0)dt

Id=12(dqdt)

Id=i2

Hence, the displacement current is i2


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