Question

A spherically symmetric charge distribution has a charge density given by ρ = a/r , where a is constant. Find the electric field within the charge distribution as a function of r. Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4πr2dr. (Use the following as necessary: a, r, and ε0. Consider that a is positive.)

Answer 1

First find charge enclosed in a closed spherical surface of radius 'r'.

\[Q = \int\limits_{0}^{r}\rho 4\pi x ^{2} dx = \int\limits_{0}^{r}a4\pi x ^{2}/x = 2\pi a r ^{2}\]

Now apply Gauss's law. Tell me if you face any problem