A metal bar AB can slide on two parallel thick metallic rails separated by a distance l. A resistance R and an inductance L are connected to the rails as shown in the figure. A long straight wire carrying a constant current `I_(0)` is placed in the plane of the rails and perpendicular to them as shown. The bar AB is held at rest at a distance `x_(0)` from the long wire. At t=0, it is made to slide on the rails away from wire. Answer the following questions.
(a) Find a relation among `i, (di)/(dt) and (d phi)/(dt)`, where i is the current in the circuit and `phi` is the flux of the megnetic field due to the long wire through the circuit.
(b) It is observed that at time t=T, the metal bar AB si at a distance of `2x_(0)` from the long wire and the resistance R carries a current `(i_1)`. Obtain an expression for the net charge that has flown through riesistance R form t=0 to t=T.
(c) THe bar is suddenly stopped at time T. THe current through resistance R is found to be `(i_1)/(4)` at time 2T. Find the value of `L/R` in terms of hte other given quantities.