Question

Derive an expression for electrostatic potential energy stored in the capacitor.

Answer 1

$$\begin{gathered} Whilecharging,tehbatterytransferschargesintothecapacitor.\hspace{0.17em}Sosomeworkdoneintransferring \\ thischarge,createssomestoredelectrostaticenergyintothecapacitor. \\ Supposethecapacitorisfullycharged,tehntheworkdoneingivinganadditionaldqchargeis \\ dW=\frac{q}{C}dq \\ W={\int }_0^Q\frac{q}{C}dq=\frac{1}{C}{\left[\frac{q^2}{2}\right]}_0^Q=\frac{1}{2}\frac{Q^2}{C} \\ soamountofelectrostaticenergy \\ U=W=\frac{1}{2}\frac{Q^2}{C} \end{gathered}$$