$A$ rod of length $l$ is rotating in the plane of the paper with an angular speed $\omega$ about one of its ends,which is at a distance $a$ from an infinitely long conducting wire carrying current $i$ inwards the plane of the paper. Find the induced $emf$ in the rod at the instant as shown in the figure.

• A
  $\frac{{{\mu _0}i\omega }}{{4\pi }}\left[ {l - a\ln \left( {\frac{{l + a}}{a}} \right)} \right]$
• B
  $\frac{{{\mu _0}i\omega }}{{2\pi }}\left[ {l - a\ln \left( {\frac{{l + a}}{a}} \right)} \right]$
• C
  $\frac{{{\mu _0}i\omega }}{{8\pi }}\left[ {l - a\ln \left( {\frac{{l + a}}{a}} \right)} \right]$
• D
  $0$