Question

Derive the expression for capacitance of parallel plate capacitor.

Answer 1

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 $E^{\prime }=\frac{\sigma }{2{ϵ}_o}$

Total electric field between the plates $E=\frac{\sigma }{2{ϵ}_o}+\frac{\sigma }{2{ϵ}_o}$

Or $E=\frac{\sigma }{{ϵ}_o}$

Or $E=\frac{Q}{A{ϵ}_o}$

Potential difference between the plates $V=Ed$

$⟹$ $V=\frac{Qd}{A{ϵ}_o}$

Capacitance $C=\frac{Q}{V}$

Thus we get capacitance of parallel plate capacitor $C=\frac{A{ϵ}_o}{d}$