$A$ conducting rod with resistance $r$ per unit length is moving inside a vertical magnetic field $\overrightarrow B$ at speed $v$ on two horizontal parallel ideal conductor rails. The ends of the rails are connected to a resistor $R$. The separation between the rails is $d$. The rod maintains a tilted angle $\theta$ to the rails. Find the external force required to keep the rod moving.

• A
  $F = \frac{{{B^2}{d^2}v}}{{(R + dr)}}$
• B
  $F = \frac{{{B^2}{d^2}v}}{{(R + dr/\sin \theta )}}$
• C
  $F = \frac{{{B^2}{d^2}v/{\sin ^2}\theta }}{{(R + dr/\sin \theta )}}$
• D
  $F = \frac{{{B^2}{d^2}v/{\cos ^2}\theta }}{{(R + dr/\cos \theta )}}$