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A parallel-plate capacitor having plate-area A and plate separation d is joined to a battery of emf ℰ and internal resistance R at t = 0. Consider a plane surface of area A/2, parallel to the plates and situated symmetrically between them. Find the displacement current through this surface as a function of time.

A parallel-plate capacitor having plate-area A and plate separation d is joined to a battery of emf ℰ and internal resistance R at t = 0. Consider a plane surface of area A/2, parallel to the plates and situated symmetrically between them. Find the displacement current through this surface as a function of time.

Grade:upto college level

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
8 years ago
Sol. E = Kq/x^2 , [from coulomb’s law] ∅ base E = EA = KqA/x^2 I base d = ϵ base 0 d∅E/dt = ϵ base 0 d/dt kqA/x^2 = ϵ base 0 KqA = d/dt x^-2 = ϵ base 0 * 1/4π ϵ base 0 *q *A * -2 *x^-3 * dx/dt = qAv/2πx^3 .

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