$A$ wire $ab$ of length $l$,mass $m$,and resistance $R$ slides on a smooth,thick pair of metallic rails joined at the bottom as shown in the figure. The plane of the rails makes an angle $\theta$ with the horizontal. $A$ vertical magnetic field $B$ exists in the region. If the wire slides on the rails at a constant speed $v$,then which of the following can be correct for $B$?

• A
  $B = \sqrt {\frac{{mgR}}{{v{l^2}\,\cos\, \theta }}} $
• B
  $B = \sqrt {\frac{{mgR\,\sin \,\theta }}{{v{l^2}\,\cos \,\theta }}} $
• C
  $B = \sqrt {\frac{{mgR\,\sin \,\theta }}{{v{l^2}\,{{\cos }^2}\,\theta }}} $
• D
  $B = \sqrt {\frac{{mgR\,\sin \,\theta }}{{v{l^2}}}}$