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

Answer

A, B, D

Explanation

Rate of work done by external agent is:
` (dW)/(dt)=(BIL.dx)/(dt)=BIL v` & 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 hence acceleration. As a result velocity increases, hence `(B)`
Since , `I=(e )/(R )`
On doubling `'R'`, current and hence required powder becomes half.
Since, `P=BILv`
Hence `(D)`