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, find the value of a.

Question

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, find the value of a.,

MARKS App · Accepted Answer

From Gauss theorem, E ∝ q r 2 (q = charge enclosed) Therefore E 2 E 1 = q 2 q 1 = r 1 2 r 2 2 or 8 = ∫ 0 R 4 π r 2 kr deg dr ∫ 0 R / 2 4 π r 2 kr deg dr × R 2 R 2 Solving this equation we get, a = 2.

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