Question

Obtain the formula for the capacitance of a parallel plate capacitor.

Answer 1

Consider a parallel plate capacitor of suface charge density $\sigma$ , surface area $A$, charge $Q$ and distance between the plate $d$.

Then, Electric Field between the plates$\left(\overrightarrow{E}\right)$ $=\frac{\sigma }{{ϵ}_0}$

$\Rightarrow$ $\overrightarrow{E}$$=\frac{Q}{A{ϵ}_0}$

$\Rightarrow$ Voltage difference between the plates$\left(V\right)$ $=\frac{Qd}{A{ϵ}_0}$

And, Capacitance$\left(C\right)$ $=\frac{Q}{V}$ $=\frac{QA{ϵ}_0}{Qd}$ $=\frac{{ϵ}_{0}A}{d}$