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 the charges on the spheres?

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

Answer 1

Answer: (B)

$\frac{r^2}{R^2}$

Let $\sigma$ is the surface density of both sphere.

Charge on the sphere of radius R is $q_R=4\pi R^2\sigma$

Charge on the sphere of radius r is $q_r=4\pi r^2\sigma$

$\frac{q_r}{q_R}=\frac{r^2}{R^2}$