As depicted in the figure, a wire PQ of mass m and resistance r can slide on smooth, horizontal parallel rails separated by a distance l . The resistance of the rails is negligible. A uniform magnetic field B exists in the rectangular region, and a resistance R connects the rails outside the field region. At t = 0 , the wire PQ is pushed towards the right with a speed v₀ . Determine the current in the loop at an inst

Step-by-step solution

When the wire PQ moves with a speed v in a uniform magnetic field B , a motional electromotive force (emf) is induced across its ends. The magnitude of this induced emf is given by: = Blv The total resistance of the closed loop is the sum of the resistance of the wire PQ and the external resistance R . Total resistance = R + r The induced current I in the loop at that instant is: I = R_ total = Blv R + r