Consider parallel conducting rails separated by a distance l. There exists a uniform magnetic field B perpendicular to the plane of the rails as shown in Fig. Two conducting wires each of length l are placed so as to slide on parallel conducting rails. One of the wires is given a velocity `v_(0)` parallel to the rails. Till steady state is achieved, loss in kinetic energy of the system is

Options

A. zero
B. `3.4 mv_(0)^(2)`
C. `1/4 mv_(0)^(2)`
D. `3/8mv_(0)^(2)`

Answer

C

Explanation

In steady state, velocity of both wires will becomes same.
`2 mv=mv_(0) implies v=v_(0)//2`
Loss in `KE=1/2 mv_(0)^(2)-2 [1/2 mv^(2)]=1/4 mv_(0)^(2)`.