# Problem: An insulating sphere of radius a, centered at the origin, has a uniform volume charge density.Find the electric field E(r) inside the sphere (for r&lt; a) in terms of the position vector r .Express your answer in terms of r  and ρ

###### FREE Expert Solution

Gauss' Law:

$\overline{){{\mathbf{\varphi }}}_{\mathbf{N}\mathbf{E}\mathbf{T}}{\mathbf{=}}\frac{{\mathbf{Q}}_{\mathbf{e}\mathbf{n}\mathbf{c}}}{{\mathbf{\epsilon }}_{\mathbf{0}}}}$

Also,

$\overline{){\mathbf{\varphi }}{\mathbf{=}}{\mathbf{E}}{\mathbf{A}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\theta }}}$

Area, A:

$\overline{){\mathbf{A}}{\mathbf{=}}{\mathbf{4}}{\mathbf{\pi }}{{\mathbf{r}}}^{{\mathbf{2}}}}$

###### Problem Details

An insulating sphere of radius a, centered at the origin, has a uniform volume charge density.

Find the electric field E(r) inside the sphere (for r< a) in terms of the position vector r .