As shown in the figure, a long, straight wire carries a current i and a rod of length l is coplanar with the wire and oriented perpendicular to it. The rod travels with a constant velocity v in a direction parallel to the wire. The distance from the wire to the centre of the rod is x . Determine the motional emf induced in the rod.

Step-by-step solution

The magnetic field produced by a long straight wire carrying current i at a distance r from it is given by: B = ₀ i 2 r The direction of the magnetic field is perpendicular to the plane containing the wire and the rod (into the page). Consider a small element of the rod of length dr at a distance r from the wire. The motional emf induced in this small element moving with velocity v is: d = B v dr Since the center of the rod is at a distance x from the wire and its total length is l , the rod extends from r = x - l