$A$ conducting rod of length $l$ moves with velocity $\upsilon$ in a direction parallel to a long wire carrying a steady current $I$. The axis of the rod is maintained perpendicular to the wire with the near end at a distance $r$ away as shown in the figure. Find the emf induced in the rod.

• A
  $\frac{{\mu _0}I\upsilon}{{2\pi }} \ln \left( {\frac{{r + l}}{r}} \right)$
• B
  $\frac{{\mu _0}I\upsilon}{\pi } \ln \left( {\frac{{r + l}}{r}} \right)$
• C
  $\frac{{\mu _0}I\upsilon}{{2\pi }} \ln \left( {\frac{r}{{r + l}}} \right)$
• D
  $\frac{{2{\mu _0}I\upsilon}}{{\pi }} \ln \left( {\frac{{r + l}}{r}} \right)$