Derive The Expression For the Capacitance Of Parallel Plate Capacitor

The expression for the capacitance of parallel plate capacitor is explained as

Place the two plates parallel to each other separated by a distance d and the cross-sectional area of each plate is A.

The electric field by a single thin plate

\(E=\frac{\sigma }{2\epsilon_0 }\)

 

The electric field between the two plates

\(E=\frac{\sigma }{2\epsilon_0 } + \frac{\sigma }{2\epsilon_0 }\)

 

The potential difference between the two plates V = Ed

⟹ \(V=\frac{Qd }{A\epsilon_0 }\)

 

Capacitance  \(C=\frac{Q }{V }\)

 

Thus we get capacitance of parallel plate capacitor

 

\(C=\frac{A\epsilon_0 }{d }\)

 

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