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: (C)

decreases as r increases for R < r < $\infty$

Answer 2

Inside the sphere $E=\frac{1}{4 \pi \varepsilon_0 }.\frac{Q}{R^3}r$
\Rightarrow\hspace20mm 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 \hspace25mm r = R
Outside the sphere
\hspace10mm 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.