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Question

Derive the expression for capacitance of parallel plate capacitor.

Solution
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Let the two plates are kept parallel to each other separated be a distance d and cross-sectional area of each plate is A.

Electric field by a single thin plate E=σ2ϵo

Total electric field between the plates E=σ2ϵo+σ2ϵo

Or E=σϵo

Or E=QAϵo

Potential difference between the plates V=Ed

V=QdAϵo

Capacitance C=QV

Thus we get capacitance of parallel plate capacitor C=Aϵod

658183_623491_ans_ab4e9627f6de4306ab7fa5c1da1849fa.png

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