Question

A hollow metal sphere of radius $R$ is uniformly charged. The electric field due to the sphere at , distance r from the centre :

• A. zero as r increases for r < R. increases as. r increases for r > R
• B. decreases as r increases for r < R and r > R
• C. increases as r increases for r < R and for r > R
• D. zero as r increases for r < R. decreases r as increases for r > R

Answer 1

Answer: (D)

Charge Q will be distributed over the surface of hollow metal sphere.
(i) For r < R (inside)
By Gauss law, $\oint {\vec{E}}_{in}.\overrightarrow{dS}=\frac{q_{en}}{{\epsilon }_0}=0$
$\Rightarrow E_{in}=0\left(\because q_{en}=0\right)$
(ii) For r > R (outside
$\oint {\vec{E}}_{in}.\overrightarrow{dS}=\frac{q_{en}}{{\epsilon }_0}$
Here, $q_{en}=Q\left(\because q_{en}=Q\right)$
$\therefore E_{0}4\pi r^2=\frac{Q}{{\epsilon }_0}$
$\therefore E_0\propto \frac{1}{r^2}$