A circular loop of radius a , carrying a current i , is situated in a two-dimensional magnetic field. The centre of the loop coincides with the centre of the field. The strength of the magnetic field at the periphery of the loop is B . Determine the magnetic force on the wire.

Step-by-step solution

Consider a small current element d l on the circular loop. The magnetic field B is radial and points outwards from the centre. The current element d l is tangential to the circular loop. The angle between the current element d l and the magnetic field B is 90^ . The magnetic force on this small element is given by d F = i(d l B ) . The magnitude of this force is dF = i B dl (90^ ) = i B dl . Using the right-hand rule, the direction of the cross product d l B is into the plane of the figure for all elements along th