Two long parallel conducting rails are separated by a distance L = 0.2 m and are connected by a resistor R = 2 at x = 0 . A conducting rod starts from x = 0 at t = 0 and slides along the rails in the positive x -direction with a constant velocity v = 2 m s ⁻¹ . The entire setup is placed in a magnetic field perpendicular to the plane of the rails, pointing outwards. The magnetic field varies with position and time as

Step-by-step solution

At t = 2 s , the position of the sliding rod is x = v t = 2 2 = 4 m . The total induced EMF in the loop is the sum of the motional EMF due to the rod's velocity and the EMF induced due to the time-varying magnetic field over the loop's area. 1. Motional EMF: The local magnetic field at the position of the rod ( x = 4 m ) at t = 2 s is: B_ local = 3 + 3(4) + 2.5(2) = 3 + 12 + 5 = 20 T _ mot = B_ local L v = 20 0.2 2 = 8 V 2. Time-varying EMF: The rate of change of the magnetic field with respect to time is B t = 2.5