Question

A uniform charged spherical shell has a total charge 2 C and radius 10 cm. With reference to infinity, self potential energy of the shell is .

• A. $1/4\pi {ϵ}_0$
• B. $5/\pi {ϵ}_0$
• C. $4/\pi {ϵ}_0$
• D. $3/\pi {ϵ}_0$

Answer 1

The correct option is B $5/\pi {ϵ}_0$

The electric self-potential energy of a uniformly charged spherical shell is given by $\frac{k{Q}^2}{2R}$ where Q is the net charge on the shell and R is the radius. The derivation of this formula can be found in the videos. Here, Q=2C and radius, R= 10cm = 0.1 m
so Self energy, $U=\frac{k{Q}^2}{2R}=k.\frac{2^2}{2\times 0.1}=k.20=\frac{5}{\pi {\epsilon }_0}$