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Electricity and Magnetism Level 3

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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