A solid sphere of radius R has a charge Q distributed in its volume with a charge density =k r^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

Question

A solid sphere of radius R has a charge Q distributed in its volume with a charge density =k r^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 .

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From Gauss theorem, aligned & E q r^2 (q= charge enclosed ) & E₂ E₁ = q₂ q₁ = r₁^2 r₂^2 & 8= ₀^R (4 r^2 ) k r^a d r ₀^ R / 2 (4 r^2 ) k r^a d r (R / 2)^2 (R)^2 & aligned Solving this equation we get, a=2

A solid sphere of radius R has a charge Q distributed in its volume with a charge density =k r^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 .

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