Walker, Halliday & Resnick — Gauss' Law: Problem 9

9 In Fig. 23-26, a nonconducting spherical shell of inner radius \( a = 1.50\text{ cm} \) and outer radius \( b = 2.40\text{ cm} \) has (within its thickness) a positive volume charge density \( \rho = A/r \), where \( A \) is a constant and \( r \) is the distance from the center of the shell. In addition, a small ball of charge \( q = 75.0\text{ fC} \) is located at that center. What value should \( A \) have if the electric field in the shell (\( a \le r \le b \)) is to be uniform?