A wire of length l, mass m, and resistance R slides without any friction down the parallel conducting rails of negligible resistance (figure). The rails are connected to
each other at the bottom by a resistanceless rail parallel to the wire so that the wire and the rails form a closed rectangular conducting loop. The plane of the rails makes
an angle $\theta$ with the horizontal and a uniform vertical magnetic field of induction B exists throughout the region. Find the steady state velocity of the wire.

• A

  $\frac{mg}{R}\frac{\sin \theta }{B^2{l}^2{\cos }^2\theta }$

• B

  $\frac{mg}{R}\frac{{\sin }^2\theta }{B^2{l}^2{\cos }^2\theta }$

• C

  $\frac{mgR\sin \theta }{B^2{l}^2{\cos }^2\theta }$

• D

  $mgR\frac{{\sin }^2\theta }{B^2{l}^2\cos \theta }$