A rigid square loop of side 20 cm and mass 240 g is hinged freely at its top horizontal edge. It hangs in a uniform vertical magnetic field of magnitude 0.5 T. When a steady current is passed through the loop, it deflects and comes to equilibrium such that its plane makes an angle of 37^ with the vertical. The current in the loop is ______ A. (Take g = 10 m/s ² )

Step-by-step solution

In equilibrium, the restoring torque due to gravity about the hinge balances the magnetic torque. Let the side of the square loop be a = 0.2 m and its mass be m = 0.24 kg. The center of mass is at a distance of a/2 from the hinge. When the loop is deflected by an angle = 37^ from the vertical, the lever arm for the gravitational force is (a/2) . Torque due to gravity: _g = mg ( a 2 ) _g = 0.24 10 ( 0.2 2 ) (37^ ) _g = 2.4 0.1 0.6 = 0.144 N.m The magnetic moment of the loop is M = I A = I a^2 . Since the plane of th