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

Step-by-step solution

Let the radius of the circular loop be r . The total length of the wire is L , so 2 r = L r = L 2 The area of the circular loop is A = r^2 = ( L 2 )^2 = L^2 4 The magnetic dipole moment of the loop is M = iA = i L^2 4 Since the magnetic field B is parallel to the plane of the loop, the angle between the magnetic moment vector (which is perpendicular to the plane) and the magnetic field is = 90^ The torque acting on the loop is = M B = ( i L^2 4 ) B 90^ = i L^2 B 4