A wire PQ with mass m and resistance r is free to slide on smooth, horizontal parallel rails separated by a distance l . The resistance of the rails is considered negligible. A uniform magnetic field B exists in the rectangular region, while a resistance R connects the rails outside the field region. At t = 0 , the wire PQ is given a push to the right with a speed v₀ . Determine the acceleration of the wire at an ins

Step-by-step solution

When the wire PQ moves with a velocity v , the motional electromotive force (emf) induced across its ends is given by: E = B l v The total resistance of the closed circuit is the sum of the resistance of the wire and the external resistance: R_ eq = R + r The induced current flowing through the circuit is: I = E R_ eq = B l v R + r The magnetic force acting on the current-carrying wire PQ in the magnetic field is: F = I l B = ( B l v R + r ) l B = B^2 l^2 v R + r According to Lenz's law, the direction of the induce