Question

Deduce an expression for the capacitance of a parallel plate capacitor.

Answer 1

• For parallel plate capacitor
  

$Q=CV$ $\to$ $V=\frac{Q}{C}$

$\sigma =\frac{Q}{A}$ ($A$=area of plates)

• Let E be the electric field between the plates
  

$E=\frac{\sigma }{ϵ}=\frac{V}{d}$ ($d$ is distance between the plates)

$\frac{Q}{Aϵ}=\frac{Q}{Cd}$

$C=\frac{Aϵ}{d}$