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. (a) The thermal power dissipated in the resistor is equal to the rate of work done by an external person pulling the rod.
B. (b) If applied external force is doubled, then a part of the external power increases the velocity of the rod.
C. ( c) Lenz's law is not satisfiedif the rod is accelerated by an external force.
D. (d) If resistance `R` is doubled, then power required to maintain the constant velocity `V_(0)` becomes half.

Answer

A, B, D

Explanation

(a, b, d):
Rate of work done by external agent is `Fv = BILv` and thermal power dissipated in the resistor `= eI = (BvL)I` clearly both are equal, hence (a).
If applied external force is doubled, the rod will experience a net force and acceleration. As a result velocity increases, hence (b)
Since, `I = (e)/(R )`
On doubling `R`, current and hence required power becomed half.
Since, `P = BILv`
Hence (d)