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A parallel plate capacitor with plate ar...

A parallel plate capacitor with plate area A and plate separation d, is charged by a steady current I. Let a plane surface of area `A//3` parallel to the plates and situated symmetrically between the plates. What is the displacement current through this area?

Text Solution

Verified by Experts

Let q be the charge on capacitor plates at any
instant t and `sigma` be the surface density of charge.
Then electric field between the plates of
capacitor will be `E=sigma/(in_0)=q/(in_0A)`
Electric flux through area `A//3` will be
`phi_E=EA/3=q/(in_0A)xxA/3=1/(3in_0)`
The displacement current will be
`I=in_0 (dphi_E)/(dt)=in_0d/(dt)(q/(3in_0))=(in_0)/(3in_0) (dq)/(dt) =I/3`
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