A straight, long wire carries a current i . Coplanar with the wire and perpendicular to it is a rod of length l . The ends of the rod slide on a pair of thick metallic rails laid parallel to the wire, and at one end the rails are connected by a resistor of resistance R . The distance of the wire from the centre of the rod is x . If the rod travels with a constant velocity v in a direction parallel to the wire, calcul

Step-by-step solution

The magnetic field produced by the long straight wire at a distance r from it is given by: B = ₀ i 2 r Consider a small element of the rod of length dr at a distance r from the wire. The motional emf induced in this element as it moves with velocity v parallel to the wire is: d = B v dr = ₀ i v 2 r dr The rod has a length l and its centre is at a distance x from the wire. Therefore, the ends of the rod are at distances r₁ = x - l 2 and r₂ = x + l 2 from the wire. The total emf induced in the rod is obtained by inte