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 \varepsilon_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 \varepsilon_0 }.\frac{Q}{R^2}$ as $r = R$ Outside the sphere
$E=\frac{1}{4 \pi \varepsilon_0 }.\frac{Q}{r^2}$
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.