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 2 R from the axis of the cylinder, is given by the expression $\frac{23 \rho \mathrm{R}}{16 \mathrm{k} \varepsilon_0}$. The value of $k$ is