Two thin rings each of radius $R$ are placed at a distance  $d$ apart. The charges on the rings are $+q$ and $-q.$ The potential difference between their centres will be -

• A

  $\frac{\mathrm{q}\mathrm{R}}{4\mathrm{\pi }{\mathrm{\epsilon }}_0{\mathrm{d}}^2}$
• Correct answer
  B

  $\frac{\mathrm{q}}{2\mathrm{\pi }{\mathrm{\epsilon }}_0}\left[\frac{1}{\mathrm{R}}-\frac{1}{\sqrt{{\mathrm{R}}^2+{\mathrm{d}}^2}}\right]$
• C

  $\mathrm{z}\mathrm{e}\mathrm{r}\mathrm{o}$
• D

  $\frac{\mathrm{q}}{4\mathrm{\pi }{\mathrm{\epsilon }}_0}\left[\frac{1}{\mathrm{R}}-\frac{1}{\sqrt{{\mathrm{R}}^2+{\mathrm{d}}^2}}\right]$

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