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 magnetic field B is directed vertically outwards from the plane of the paper (indicated by dots). The wire ab moves with velocity v towards the right. The motional emf induced across the wire is given by e = Bvl . The direction of the motional emf is given by v B . Since v is towards the right ( i ) and B is outwards ( k ), the direction of positive charge flow is i k = - j (downwards, from a to b ). Thus, the motional emf acts as a source driving current from a to b . The battery has its positive terminal conn