Question

Two long parallel horizonal rails , a distance d apart and each having a resistance `lambda` per unit length are jointed at one end by a resitance R. A perfectly conducting rod MN of mass m is free to slide along the rails . A variable force F is applied to the rod MN , such that ,as the rd moves, a constant current i flows through R.
(a) Find the velocity v and the force F as function of the function of the distance x of the rod from R.

(b) What fraction `eta` of the work done by F per second in converted into heat ?

Answer 1

Correct Answer - `v=((R+ 2xlambda)i)/(Bd) F=B+(2mlambdar^(2)(R + 2 x lambda))/(B^(2)d^(2)),eta =(R)/((R+2 x lambda)+(2 lambdax (R+2x lambda )^(2))/(B^(3)d^(3)