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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 A2 parallel to the plates and drawn symmetrically between the plates. Find the displacement current through this area.

A
i4
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B
i2
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C
i
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D
Zero
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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=E×A2=Qε0A×A2=Q2ε0

The displacement current is given by

Id=ε0dϕEdt

Id=ε0(12ε0)dQdt

Id=i2

Hence, option (B) is correct.

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