Question

The electric field due to a uniformly charged sphere of radius $R$ as a function of the distance from its centre is represented graphically by

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

$E_{\text{inside }}=\frac{\rho }{3{\epsilon }_0}r(r<R)$
$E_{\text{outside }}=\frac{\rho R^3}{3{\epsilon }_0{r}^2}(r\ge R)$
i.e. inside the uniformly charged sphere field varies linearly $(E\propto r)$ with distance and outside varies
according to $E\propto \frac{1}{r^2}$
Aliter: Outside the spherical charge, the intensity of electric field at a distance $r$ from the centre of the charge, $E=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r^2}$ (if $r>R)$
On the surface of spherical charge, $E=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r^2}$
and inside the spherical charge the electric field
$E=\frac{1}{4\pi {\epsilon }_0}\frac{qr}{R^3}$ (if $r<R)$