JEE Main · 2023 · 08 Apr 2023 · Shift 1 · Electrostatics

Apply Gauss's law to the uniformly charged insulating solid sphere. Inside the sphere $(r\le R)$ the charge enclosed grows as $r^3$, giving $E=\frac{1}{4\pi {ϵ}_0}\frac{Qr}{R^3}$, so the field rises linearly with $r$. Outside the sphere $(r\ge R)$ the entire charge behaves as if concentrated at the centre, giving $E=\frac{1}{4\pi {ϵ}_0}\frac{Q}{r^2}$, which falls off as $1/r^2$. The field therefore increases along a straight line to its maximum at $r=R$ and then decreases hyperbolically for $r>R$.