Question

A non-conducting solid sphere of radius $R$ is uniformly charged. The magnitude of the electric field due to the sphere at a distance $r$ from its centre

• A. increases as r increases for r < R
• B. decreases as r increases for 0 < r < $\infty$
• C. decreases as r increases for R < r < $\infty$
• D. is discontinuous a r = R

Answer 1

Answer: (A), (C)

Inside the sphere $E=\frac{1}{4\pi {\epsilon }_0}.\frac{Q}{R^3}r$
$\Rightarrow E\propto r$ for $r\le R$
i.e. $E$ at centre $=0$ as $r=0$ and $E$ at surface $=\frac{1}{4\pi {\epsilon }_0}.\frac{Q}{R^2}$ as $r=R$ Outside the sphere
$E=\frac{1}{4\pi {\epsilon }_0}.\frac{Q}{r^2}$
for $r\ge R$ or $E\propto \frac{1}{r^2}$
Thus, variation of electric field $(E)$ with distance $(r)$ from the centre will be as shown.