A current (i) carrying infinite wire of mass m is placed on 2 horizontal rails 'd' distance apart. a) What is the direction of current if u consider the rails to be in the XY plane?b) What is the minimum magnetic field that should exist in this region to slide the wire if coeff. of friction between rails and wire is?i repeat - minimum magnetic field.

As long as the rod moves at a constant speed, all the work done by external person the rod is dissipated as heat in the resistor. As per Work-energy theorem, there is no change in kinetic energy of rod.
Here, force applied by external agent isF=F=BIl.
However, if applied external force is doubled then a part of external power increases the velocity of rod the rest is dissipated as heat.
Obviously, Lenz's law is not satisfied under such circumstances. Further,P=E2/R=B2l2/RP=E2/R=B2l2/R. Thus, if resistance R is doubled then power required to maintain the constant velocityv0v0becomes half.