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

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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 π r^ 2 d r or E × 4 π R^ 2 =( 4 π k _ 0 ) R^ (a+3) (a+3) E_ 1 = k R^ (a+1) _ 0 (a+3) For r=(R)/(2) · E_ 2 = k((R)/(2))^ a+1 _ 0 (a+3) Given, E_ 2 = E_ 1 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

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