Question

Assuming that a positive charge $Q$ is uniformly distributed over the surface of a shell, the field at a distance $r$ from the centre of the shell where $r=3R$ ($R$ being the radius of the shell), is

• A. $\frac{Q}{{\epsilon }_{0}4\pi (2R{)}^2}$
• B. $\frac{Q}{{\epsilon }_{0}4\pi R^2}$
• C. $\frac{Q}{{\epsilon }_{0}4\pi (3R{)}^2}$
• D. none of these

Answer 1

Answer: (C)

It is as if the whole charge is concentrated at the centre of the shell.
By Gauss's theorem,
$E=\frac{Q}{{\epsilon }_0(4\pi r^2)}$
$=\frac{Q}{{\epsilon }_{0}4\pi (3R{)}^2}(\because r=3R)$