The region between two concentric spheres of radii $‘a’$ and $‘b’$, respectively (see figure), has volume charge density $\rho = \large\frac{A}{r}$, where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is :

Question

$\begin{array}{1 1} (1) \Large\frac{Q}{2 \pi a^2} \\ (2) \Large\frac{Q}{2 \pi (b^2-a^2)} \\ (3) \Large\frac{2Q}{ \pi (a^2-b^2)} \\ (4) \Large\frac{2Q}{ \pi a^2} \end{array}$