Field inside a charged ball

Find the magnitude of the electric field at the center of a ball of radius R R with volume charge density ρ = a r , \rho = \vec{a}\cdot\vec{r}, where r \vec{r} is the radius vector drawn from the ball's center and a \vec{a} is a constant vector.


Details and Assumptions:

  • a a denotes the magnitude of a \vec{a} .
a R 2 6 ϵ 0 \frac{aR^2}{6\epsilon_{0}} a R 2 2 ϵ 0 \frac{aR^2}{2\epsilon_{0}} a R 2 12 ϵ 0 \frac{aR^2}{12\epsilon_{0}} a R 2 3 ϵ 0 \frac{aR^2}{3\epsilon_{0}}

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