The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density $\mathrm{\rho }=\frac{\mathrm{A}}{\mathrm{r}}$ , 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:

• A

  $\frac{2\mathrm{Q}}{\mathrm{\pi }\left({\mathrm{a}}^2-{\mathrm{b}}^2\right)}$
• B

  $\frac{2\mathrm{Q}}{\mathrm{\pi }{\mathrm{a}}^2}$
• Correct answer
  C

  $\frac{\mathrm{Q}}{2\mathrm{\pi }{\mathrm{a}}^2}$
• D

  $\frac{\mathrm{Q}}{2\mathrm{\pi }\left({\mathrm{b}}^2-{\mathrm{a}}^2\right)}$

Hence, the correct answer is option: 'C'.