Q amount of electric charge is present on the surface of a sphere having radius R. Calculate the total energy of the system.

Options

A. `(kQ^(2))/(R)`
B. `(1)/(2) (kQ^(2))/(R)`
C. `(kQ^(2))/(R^(2))`
D. `(1)/(2) (kQ^(2))/(R^(2))`

Answer

A, B

Explanation

When there is no charge on the sphere `V_((0))` =0 and Q charge on sphere electric potential `V_((Q))= (kQ)/(R)`
`:.` Average electric potential V
`= (V_(0)+V_(Q))/(2) = (kQ)/(2R)`
`:.` Potential energy `U = VQ = (kQ^(2))/(2R)`