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 $r=3\, R$ ($R$ being the radius of the shell), is

• A. $\frac{Q}{\varepsilon_{0} 4 \pi(2 R)^{2}}$
• B. $\frac{Q}{\varepsilon_{0} 4 \pi R^{2}}$
• C. $\frac{Q}{\varepsilon_{0} 4 \pi(3 R)^{2}}$
• 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}{\varepsilon_0(4\pi r^2)} $
$= \frac{Q}{\varepsilon_0 4\pi (3R)^2} (\because r = 3R)$