A conducting circular ring and a conducting elliptical ring both are moving pure translationally in a uniform magnetic field of strength B as shown in figure on a horizontal conducting plane then potential difference between top most points of circle and ellipse is :

Points 1 and 3 connected to same conducting plane so ${\text{v}}_{\text{2}}{\text{=v}}_{\text{3}}$

Now

$\begin{array}{c}{\text{v}}_{\text{3}}{\text{-v}}_{\text{4}}\text{=B}\left(\text{2v}\right)\left(\text{2a}\right)\text{:}{\text{v}}_{\text{1}}{\text{-v}}_{\text{2}}\text{=B}\left(\text{2v}\right)\left(\text{4a}\right)\\ \therefore {\text{v}}_{\text{3}}{\text{-v}}_{\text{4}}\text{=4Bva}\mathrm{.....}\left(\text{1}\right)\text{:}{\text{v}}_{\text{1}}{\text{-v}}_{\text{2}}\text{=8Bva}\mathrm{.....}\left(\text{2}\right)\end{array}$

$\therefore \left(2\right)-\left(1\right)$        

$\begin{array}{c}{\text{v}}_{\text{1}}{\text{-v}}_{\text{2}}\text{=8Bva}\\ {\text{v}}_{\text{3}}{\text{-v}}_{\text{4}}\text{=4Bva}\\ \left(\text{-}\right)\left(\text{+}\right)\text{-}\end{array}$              $\left[\because {\text{v}}_{\text{1}}{\text{-v}}_{\text{3}}\right]$

$\begin{array}{c}\text{\_\_\_\_\_\_\_\_\_\_\_}\\ {\text{v}}_{\text{4}}{\text{-v}}_{\text{2}}\text{=4Bva}\\ \text{\_\_\_\_\_\_\_\_\_\_\_}\end{array}$

$\therefore$  ${\text{v}}_{\text{4}}{\text{-v}}_{\text{2}}\text{=4Bva}$