Question

There is a hollow sphere of charge Q and radius R. The self-potential energy of the sphere is proportional to

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

Answer 1

Answer: (B), (C)

$\frac{1}{R}$

Go back to the videos if you don’t remember how we got the self-potential energy of a hollow sphere. It’s given by $\frac{K{Q}^2}{2R}$
Hence it is proportional to $Q^2$ and $\frac{1}{R}$.
Or if we simply use dimensional analysis, after K, we have to have remaining dimensions forming $\frac{Q^2}{R}$. Since only Q and R terms are there in the option, the answer is obvious.