As shown in the figure, a long U-shaped wire of width l is situated in a perpendicular magnetic field B . A wire of length l is slid along the U-shaped wire towards the right at a constant velocity v . All wires possess a resistance of r per unit length. At t = 0 , the sliding wire is located near the left edge of the U-shaped wire. Determine the current flowing in the circuit at time t .

Step-by-step solution

The motional EMF induced in the sliding wire moving with velocity v in a perpendicular magnetic field B is given by: E = Blv At time t , the distance moved by the sliding wire is x = vt . The circuit forms a rectangular loop. The total length of the wire forming this loop consists of the left edge of the U-shaped wire (length l ), the sliding wire (length l ), and the top and bottom horizontal segments (each of length vt ). The total length of the conducting loop at time t is: L = l + l + vt + vt = 2(l + vt) Since