A conducting rod of length is moved at constant velocity `v_(0)` on two parallel, conducting, smooth, fixed rails, that are placed in a uniform constant magnetic field B perpendicular to the plane for the rails as shown in Fig. A resistance R is connected between the two ends of the rails.
Then which of the following is/are correct:

Options

A. Th thermal power dissipated in the resistor is equal to rate of work done by externl person pulling the rod.
B. If applied external force is doubled then a part of external power increases the velocity of rod.
C. Lenz's Law is not satisfied if the rod is accelerated by external force
D. If resistance R is doubled then power required to maintain the constant velocity `v_(0)` becomes half.

Answer

A, B, D

Explanation

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 is `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=E^(2)//R=B^(2)l^(2)//R`. Thus, if resistance R is doubled then power required to maintain the constant velocity `v_(0)` becomes half.