Electrostatics

An infinitely long solid cylinder of radius R has a uniform volume charge density \(\rho\). It has a spherical cavity of radius R/2 with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point P, which is at a distance 2R from the axis of the cylinder, is given by the expression \({{23\rho R} \over {16k{\varepsilon _0}}}\). The value of k is _____________.