A long U-shaped wire of width l is positioned in a perpendicular magnetic field B . A wire of length l slides on the U-shaped wire towards the right at a constant velocity v . The resistance of all the wires is r per unit length. At t = 0 , the sliding wire is situated close to the left edge of the U-shaped wire. If the force required just after t = 0 to maintain this motion is F₀ , find the time at which the require

Step-by-step solution

The motional emf induced in the sliding wire is given by: E = Bvl Let the position of the sliding wire at time t be x = vt . The conducting loop is formed by the left edge of the U-shaped wire (length l ), the top and bottom horizontal segments (each of length vt ), and the sliding wire (length l ). The total length of the conducting loop at time t is: L(t) = l + vt + vt + l = 2l + 2vt Since the resistance of all wires is r per unit length, the total resistance of the loop at time t is: R(t) = r(2l + 2vt) = 2r(l +