A solid sphere of radius R has a charge Q distributed in its volume with a charge density ρ = kr a , where k and a are constants and r is the distance from its centre. If the electric field at r = R 2 is 1 8 times that at r = R , then find the value of a

Step-by-step solution

From Gauss' theorem, E ∝ q r 2                q = charge   enclosed E 2 E 1 = q 2 q 1 = r 1 2 r 2 2 8 = ∫ 0 R 4 πr 2 kr a dr ∫ 0 R / 2 4 πr 2 kr a dr × R 2 2 R 2 Solving this equation we get, a = 2 .