question_answer 40)

  A conducting wire XY of mass m and negligible resistance slides smoothly on two parallel conducting wires as shown in Fig. 4(EP).12. The closed circuit has a resistance R due to AC. AB and CD are perfect conductors. There is a magnetic field B =. (i) Write down equation for the acceleration of the wire XY. (ii) If B is independent of time, obtain (t), assuming (0) = . (iii) For (b), show that the decrease in kinetic energy of XY equals the heat lost in R.

Answer:

                  Fig. 4(EP).12 shows a conducting wire XY of mass m and negligible resistance sliding smoothly over two parallel conducting wires AB and CD. The magnetic field applied is (i) At time t, suppose XY is at  = (t) Magnetic flux associated with area ACYX emf induced,  current induced, Force on-XY, or     ...... using (i)  Acceleration of wire ;        ??..(ii) (ii) When B is independent of time, it is constant w.r.t. time. Therefore, . From (ii), or  .  At t = 0,     ??..(iii) (iii) Now,  using (iii), Power lost = = decrease in KE of wire XY, which was to be proved.