Question

A sphere of radius R carries a charge of volume charge density ρ= ar, where a is a

constant and r denotes the distance from the centre of the sphere. Calculate the

total charge enclosed by the sphere and the electric field at points lying inside and

outside the sphere.

Answer 1

$\rho=ar,$

$E(4\pi r^2)=\frac{\int\rho\cdot4\pi r^2dr}{\varepsilon_0}=\frac{\int ar\cdot4\pi r^2dr}{\varepsilon_0},$

$E=\frac{ar^2}{4\varepsilon_0}.$