A wire with a total length L is used to form a square loop carrying a current i . A uniform magnetic field B is present parallel to the plane of the loop. Determine the torque on the square loop.

Step-by-step solution

Let the side length of the square loop be a . Since the total length of the wire is L , the perimeter of the square is 4a = L a = L 4 . The area of the square loop is A = a^2 = ( L 4 )^2 = L^2 16 . The magnetic dipole moment of the loop is M = iA = iL^2 16 . The magnetic field B is parallel to the plane of the loop, so the angle between the area vector of the loop and the magnetic field is = 90^ . The magnitude of the torque on the loop is = MB . Substituting the values, we get = ( iL^2 16 )B 90^ = iL^2B 16 .