Let a total charge $2\mathrm{Q}$ be distributed in a sphere of radius $\mathrm{R},$ with the charge density given by $\rho \left(\mathrm{r}\right)=\mathrm{k}\mathrm{r},$ where $\mathrm{r}$ is the distance from the centre. Two charges $\mathrm{A}$ and $\mathrm{B}$ , of $-\mathrm{Q}$ each, are placed on diametrically opposite points, at equal distance, a, from the centre. If $\mathrm{A}$ and $\mathrm{B}$ do not experience any force, then:

• A

  $\mathrm{a}=\frac{3\mathrm{R}}{2^{\frac{1}{4}}}$
• B

  $\mathrm{a}=\frac{\mathrm{R}}{\sqrt{3}}$
• C

  $\mathrm{a}=2^{\frac{-1}{4}}\mathrm{R}$
• Correct answer
  D

  $\mathrm{a}=8^{\frac{-1}{4}}\mathrm{R}$

Hence, the correct answer is option: 'D'.