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Q.
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
Electric Charges and Fields
Solution:
$E_{\text {inside }}=\frac{\rho}{3 \varepsilon_{0}} r (r < R) $
$ E_{\text {outside }}=\frac{\rho R^{3}}{3 \varepsilon_{0} r^{2}} (r \geq 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, $E=\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{r^{2}}$ (if $r>R)$
On the surface of spherical charge, $E=\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{r^{2}}$
and inside the spherical charge the electric field
$E=\frac{1}{4 \pi \varepsilon_{0}} \frac{q r}{R^{3}} $ (if $\left.r < R\right)$
