Question

Calculate the elctric field at a distance 'r' from the center of a uniformly charged solid sphere of radius 'R' when r < R. The charge density is given by ρ

ρ. 

Answer 1

Radius of the sphere =R

The charge density =$\rho$

Charge on the sphere =

$\rho\times V=\frac{4}{3} \pi R^3\times \rho$

For r<R using Gauss law we have,

$E(4 \pi r^2) = \frac{1}{\epsilon 0} \times$ $\frac{4}{3} \pi R^3\times\rho$

Simplifying for electric field, we have,

$E=\frac{1}{4\pi \epsilon0} \frac{Q}{R^3} r$