# Hole in the cylinder

Electricity and Magnetism Level 4

An infinitely long solid cylinder of radius $$\ell$$ has a charge density $$\rho$$. It has a spherical cavity of radius $$\frac {\ell}{2}$$ with its centre on the axis of the cylinder. The magnitude of the electric field at a distance of $$2\ell$$ from the axis of the cylinder is given by $$\frac {a\rho\ell}{b\epsilon_o}$$.

Find the value of $$a + b$$.

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