question_answer 45)

  A rod of mass m and resistance R slides smoothly over two parallel perfectly conducting wires kept sloping at an angle with respect to the horizontal, Fig. 4(EP).19. The circuit is closed through a perfect conductor at the top. There is a constant magnetic field B along the vertical direction. If the rod is initially at rest, find the velocity of the rod as a function of time.

Answer:

                  The set up is shown in Fig. 4(EP).19. Component of weight of rod down the incline = mg sin. Component Of magnetic field up          the incline = B cos. Therefore, force on the rod due to magnetic field =                                                                     The equation of motion of the rod can be written as  or where A is a constant that can be determined from initial conditions (A = 1).