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:

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

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* .

Express your answer in terms of *r* and ρ

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