Question

$Q$ amount of electric charge is present on the surface of a sphere having radius $R$. Then electrical potential energy of this system is

• A. $\frac{K{Q}^2}{R^2}$
• B. $\frac{K{Q}^2}{R}$
• C. $\frac{1}{2}\frac{K{Q}^2}{R}$
• D. $\frac{1}{2}\frac{K{Q}^2}{R^2}$

Answer 1

The correct option is C $\frac{1}{2}\frac{K{Q}^2}{R}$

We know that
The energy $U$ which is stored in the capacitor
$U=\frac{1}{2}\frac{Q^2}{C}$ $[\because C=4\pi {\epsilon }_0\cdot R;K=\frac{1}{4\pi {\epsilon }_0}]$
$U=\frac{1}{2}\frac{Q^2}{R/K}\Rightarrow U=\frac{1}{2}\frac{K{Q}^2}{R}$