Question

A charge q is distributed over two spheres of radii R and r such that their surface densities are equal. What is the ratio of their potentials?

• A. $\frac{R}{r}$
• B. $\frac{R^2}{r^2}$
• C. $\frac{R^3}{r^3}$
• D. $\frac{R^4}{r^4}$

Answer 1

The correct option is A $\frac{R}{r}$

Potential for sphere of radius R is $V_R=\frac{k{q}_R}{R}=\frac{k\sigma .4\pi R^2}{R}=k\sigma .4\pi R$ where $\sigma =$ surface charge density.

Potential for sphere of radius r is $V_r=\frac{k{q}_r}{r}=\frac{k\sigma .4\pi r^2}{R}=k\sigma .4\pi r$

thus, $\frac{V_R}{V_r}=\frac{R}{r}$