# It's Gaussy time.

A ball of radius $$R$$ is charged with a volume charge density which with the distance $$r$$ from the centre as $$\rho = \alpha r^2$$ where $$\alpha$$ is a positive constant. The magnitude of electric field intensity at a distance $$r = \dfrac{R}{2}$$ is given by:

$$\large E = \dfrac{a \alpha R^3}{b \epsilon_0}$$

$$a$$ and $$b$$ are co-prime.

What is $$a+b \ ?$$

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