A current-carrying wire joining two fixed points a and b is placed in a uniform magnetic field. The force acting on the wire is:

Step-by-step solution

The magnetic force on a small element d l of the wire carrying current I in a magnetic field B is given by d F = I(d l B ) . The total force on the wire from point a to point b is obtained by integrating the force over the entire length of the wire: F = _ a ^ b I(d l B ) Since the magnetic field B is uniform, it is constant and can be taken out of the integral: F = I ( _ a ^ b d l ) B The integral _ a ^ b d l is simply the displacement vector L from the initial point a to the final point b . F = I( L B ) This expre