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}}{\varepsilon_{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}}{\varepsilon_{0}} $
Here, $ q_{en} = Q \left(\because q_{en} =Q\right) $
$ \therefore E_{0} 4\pi r^{2} = \frac{Q}{\varepsilon_{0}} $
$ \therefore E_{0} \propto \frac{1}{r^{2}} $