The gap between the plates of a parallel plate capacitor of area A and distance between plates d , is filled with a dielectric whose relative permittivity varies linearly from ϵ 1 at one plate to ϵ 2

Question

The gap between the plates of a parallel plate capacitor of area A and distance between plates d , is filled with a dielectric whose relative permittivity varies linearly from ϵ 1 at one plate to ϵ 2 at the other. The capacitance of the capacitor is

TestHub · Accepted Answer

1 d C = d x ϵ 0 ϵ A = d x ϵ 0 ϵ 1 + ϵ 2 - ϵ 1 d x A 1 C = ∫ 1 d C = 1 ∈ 0 A ∫ 0 x d x ∈ 1 + ∈ 2 - ∈ 1 d = ln ∈ 2 / ∈ 1 d ∈ 0 A ∈ 2 - ∈ 1 C = ∈ 0 A ∈ 2 - ∈ 1 ln ∈ 2 / ∈ 1 · d

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