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Question

The area of the plates of a parallel plate capacitor is A and the gap between them is d. The gap is filled with a non-homogeneous dielectric whose dielectric constant varies with the distance yfrom one plate as : K = λsec(πy2d) , where λ is a dimensionless constant. The capacitance of this capacitor is

A
πϵ0λA2d
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B
πϵ0λAd
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C
2πϵ0λAd
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D
None
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Solution

The correct option is A πϵ0λA2d
Ey=σkyϵ0

dV=σkϵ0dy

dV=σλϵ0cos(πy2d)dy

Integrating to dy and other side;

V0dV=d0σλϵ0cos(πy2d)dy

V=σλϵ0.2dπ

C=Qσ(λϵ0π2d)

C=Aλϵ0π2d

973060_956264_ans_1555b3f498c142898d2570abbdc70e36.png

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