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Module 2 : Electrostatics

Lecture 10 : Capacitance

This is the amount of energy stored in the capacitor.
One can also get the same expression by using the expression for the energy of a charge distribution derived earlier

For a parallel plate capacitor $E = Q/A\epsilon_0$ within the volume of the capacitor and zero outside. Hence

$\begin{eqnarray*} W &=& \frac{\epsilon_0}{2}\left(\frac{Q}{A\epsilon_0}\right)^2\cdot Ad \\ &=& \frac{Q^2d}{2\epsilon_0 A} = \frac{Q^2}{2C} \end{eqnarray*}$

Exercise 1