Two long parallel horizontal rails, a distance l apart and each
has a resistance $\lambda$ per unit length are joined at one end by a
resistance R. A perfectly conducting rod MN of mass m is free to
slide along the rails without friction. There is a uniform magnetic
field of induction B normal to the plane of paper and directed
into the paper. A variable force F is applied to the rod MN such
that, as the rod moves, a constant current i flows through R.
What is the fraction of work per second by F is converted into heat.