A smooth pair of thick metallic rails is connected across a battery of emf E with negligible internal resistance. A wire ab having length l and resistance r can slide smoothly on these rails. The whole system is situated in a horizontal plane and placed in a uniform vertical magnetic field B . At a certain instant t , the wire is imparted a small velocity v towards the right. After some time, the wire ab will slide w

Step-by-step solution

The battery has its positive terminal connected to the upper rail, so it drives a current through the wire from a to b . The wire ab moves towards the right with velocity v in a uniform magnetic field B directed outwards (out of the plane of the paper). The motional emf induced in the wire is given by e = Bvl . The direction of this induced emf can be found using the relation E _ ind = v B . Since v is towards the right and B is outwards, the cross product v B points downwards, i.e., from a to b . Alternatively, by