A wire carrying a current i is positioned in the x – y plane along the curve y = A ( 2 x ) . A magnetic field B is present in the z -direction. Determine the magnitude of the magnetic force acting on the section of the wire between x = 0 and x = .

Step-by-step solution

The magnetic force on a current-carrying wire in a uniform magnetic field is given by F = i (d l B ) . Since the magnetic field B = B k is uniform, the total force depends only on the displacement vector L between the initial and final points of the wire. The initial point at x = 0 is (0, 0, 0) . The final point at x = is ( , A (2 ), 0) = ( , 0, 0) . The displacement vector is L = i . The magnetic force is F = i ( L B ) = i ( i B k ) = -i B j . The magnitude of the magnetic force is | F | = i B .