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, the value of a

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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, the value of a is

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Correct answer: C. 2

Using Gauss's law, we have E d A = 1 ₀ ( d v)= 1 ₀ ₀^ R k r^ a 4 r² d r or E 4 R²= ( 4 k ₀ ) R^ (a+3) (a+3) E₁= k R^ (a+1) ₀(a+3) For r= R 2 E₂= k ( R 2 )^ a+1 ₀(a+3) Given, E₂= E₁ 8 or k ( R 2 )^ a+1 ₀(a+3) = 1 8 k R^ (a+1) ₀(a+3) array ll & 1 a+1 = 1 8 or & a=2 . array

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, the value of a is

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