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 I0 is placed in the plane of the rails and perpendicular to them as shown. The bar AB is held at rest at a distance x0 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,didtanddϕdt, where i is the current in the circuit and ϕ 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 2×0 from the long wire and the resistance R carries a current (i1). 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 i14 at time 2T. Find the value of LR in terms of hte other given quantities.