A uniformly charged solid non-conducting sphere of radius $R$ has an electric field $E$ at a distanc

Question

A uniformly charged solid non-conducting sphere of radius $R$ has an electric field $E$ at a distance $\frac{R}{2}$ from the centre. What is the magnitude of the electric field at a distance $2R$ from the centre of the sphere?

Professor PC Thomas Classes · Answer

(a) : The electric field inside a solid non-conducting sphere is $E_{in} = \frac{kQr}{R^3}$. At $r = R/2$, $E = \frac{kQ(R/2)}{R^3} = \frac{kQ}{2R^2}$, which gives $kQ = 2ER^2$. The electric field outside the sphere is $E_{out} = \frac{kQ}{r^2}$. At $r = 2R$, the field is $E^{\prime} = \frac{kQ}{(2R)^2} = \frac{kQ}{4R^2}$. Substituting $kQ = 2ER^2$, we get $E^{\prime} = \frac{2ER^2}{4R^2} = \frac{E}{2}$.