Let a total charge \( 2 Q \) be distributed in a sphere of radius \( R \), with the charge densi...

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Let a total charge \( 2 Q \) be distributed in a sphere of radius \( R \), with the charge density given by \( \rho(r)=k r \), where \( r \) is the distance from the center. Two charges \( A \) and \( B \), of \( -Q \) each, are placed on diametrically opposite points, at equal distance, a, from the center. If \( A \) and \( B \) do not experience any force, then
(a) \( a=\frac{3 R}{2^{1 / 4}} \)
(b) \( a=R / \sqrt{3} \)
(c) \( a=8^{-1 / 4} R \)
(d) \( a=2^{-1 / 4} \mathrm{R} \)
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