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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