Two identical thin rings each of radius R are placed co-axially at a distance R apart. If ${\mathrm{Q}}_1 \mathrm{and} {\mathrm{Q}}_2$ are respectively the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of the other is :

• A

  Zero

• B

  $\frac{\mathrm{q}\left({\mathrm{Q}}_1-{\mathrm{Q}}_2\right)\left(\sqrt{2}-1\right)}{4{\mathrm{\pi \epsilon }}_0 \sqrt{2}\mathrm{R}}$

• C

  $\frac{\mathrm{q}\left({\mathrm{Q}}_1+{\mathrm{Q}}_2\right)}{ 4{\mathrm{\pi \epsilon }}_0 } \mathrm{x} \frac{\sqrt{2}}{\mathrm{R}}$

• D

  $\frac{\mathrm{q}\left({\mathrm{Q}}_1+{\mathrm{Q}}_2\right)}{4{\mathrm{\pi \epsilon }}_0 } \mathrm{x} \frac{\left(\sqrt{2}+1\right)}{ \sqrt{2}\mathrm{R}}$