A circular ring with area 4.45 cm² is carrying a current of 11.5 A. The ring, initially at rest, is immersed in a region of uniform magnetic field given by B = (1.35 × 10-²T) (12î +3j – 4k). The ring is positioned initially such that its magnetic moment orientation is given by μ₁ −μ(-0.82 +0.63), where is the (positive) magnitude of the magnetic moment. (a) Find the initial magnetic torque on the ring. (b) The ring (which is free to rotate around one diameter) is released and turns through an angle of 90.0°, at which point its magnetic moment orientation is given by μ = μk. Determine the decrease in potential energy. (c) If the moment of inertia of the ring about a diameter 4.50 x 10-7 kg - cm², determine the angular speed of the ring as it passes through the second position.

A circular ring with area 4.45 cm² is carrying a current of 11.5 A. The ring, initially at rest, is immersed in a region of uniform magnetic field given by B = (1.35 × 10-²T) (12î +3j – 4k). The ring is positioned initially such that its magnetic moment orientation is given by μ₁ −μ(-0.82 +0.63), where is the (positive) magnitude of the magnetic moment. (a) Find the initial magnetic torque on the ring. (b) The ring (which is free to rotate around one diameter) is released and turns through an angle of 90.0°, at which point its magnetic moment orientation is given by μ = μk. Determine the decrease in potential energy. (c) If the moment of inertia of the ring about a diameter 4.50 x 10-7 kg - cm², determine the angular speed of the ring as it passes through the second position.