$A$ conducting rod with resistance $r$ per unit length is moving inside a vertical magnetic field $\vec B$ at constant 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
  $F=\frac{B^2d^2v}{(R+dr)}$
• B
  $F=\frac{B^2d^2v}{(R+dr/\sin \theta)}$
• C
  $F=\frac{B^2d^2v/\sin \theta}{(R+dr/\sin \theta)}$
• D
  $F=\frac{B^2d^2v/\cos^2 \theta}{(R+dr/\cos \theta)}$