A solid non-conducting sphere of radius $R$ has a uniform volume charge density $\rho$. The magnitud

Question

A solid non-conducting sphere of radius $R$ has a uniform volume charge density $\rho$. The magnitude of the electric field $E$ due to the sphere at a distance $r$ from the centre

Professor PC Thomas Classes · Answer

(a) : For a uniformly charged solid non-conducting sphere, the electric field at an internal point ($r < R$) is given by $E = \frac{\rho r}{3\varepsilon_0}$, which means $E \propto r$ (increases linearly). At an external point ($r > R$), the sphere behaves as a point charge, so $E = \frac{Q}{4\pi\varepsilon_0 r^2}$, which means $E \propto \frac{1}{r^2}$ (decreases parabolically).