Two identical uniform wires, each of length L , are bent to form a single-turn circular loop and a single-turn square loop, respectively. Both loops carry the same steady current I and are placed in a uniform magnetic field B such that the plane of each loop is parallel to the magnetic field. The ratio of the maximum magnetic torque experienced by the circular loop to that experienced by the square loop is:

Step-by-step solution

The magnetic torque experienced by a current-carrying loop in a uniform magnetic field is given by = MB , where M is the magnetic dipole moment and is the angle between the area vector and the magnetic field. Since the plane of each loop is parallel to the magnetic field, the angle = 90^ , and the torque is maximum: = MB . For the circular loop of length L : 2 R = L R = L 2 Magnetic moment, M_ circle = I R^2 = I ( L 2 )^2 = IL^2 4 For the square loop of length L : 4a = L a = L 4 Magnetic moment, M_ square = I a^2 =