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

Moderate

Solution

$E_{inside} = \frac{ρ}{3 ε_{0}} r (r < R) E_{outside} = \frac{{ρR}^{3}}{3 ε_{0} r^{2}} (r \geq R)$
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
$E = \frac{1}{4 {πε}_{0}} \frac{q}{r^{2}} (if r > R)$
On the surface of spherical charge, $E = \frac{1}{4 {πε}_{0}} - \frac{q}{r^{2}}$
and inside the spherical surface the electric field
$E = \frac{1}{4 {πε}_{0}} \frac{qr}{R^{3}} (if r < R)$

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