Question

A uniformly charged sphere, entirely made up of charges in vacuum, has a total charge 20 C and radius 10 mm. With reference to infinity, what is the self-potential energy of the system?

• A. $\frac{6000J}{\pi {ϵ}_0}$
• B. $\frac{5000J}{\pi {ϵ}_0}$
• C. $\frac{24000J}{\pi {ϵ}_0}$
• D. $\frac{25000J}{\pi {ϵ}_0}$

Answer 1

The correct option is A $\frac{6000J}{\pi {ϵ}_0}$

The electric self-potential energy of a uniformly charged sphere is given by $\frac{3k{Q}^2}{5R}$ where Q is the net charge on the sphere and R is the radius. The derivation of this formula can be found in the videos. I encourage you to go through it in case you haven’t already.After you derive this(or recall it) the only job is to plug in the values in S.I units and find the answer. Here, Q=20C and radius, R= 10mm = 0.01 m
So Self energy, $U=\frac{3k{Q}^2}{5R}=k.\frac{3\times {20}^2}{5\times 0.01}=k.24000=\frac{6000}{\pi {\epsilon }_0}$