Question

A circular ring with area 4.45 cm2 is carrying a current of 12.5 A. The ring, initially at rest, is immersed in a region of uniform magnetic field given by B⃗ =(1.25×10−2T)(12i^+3j^−4k^). The ring is positioned initially such that its magnetic moment orientation is given by μ⃗ i=μ(−0.8i^+0.6j^), where μ 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 μ⃗ f=−μk^. Determine the decrease in potential energy. (c) If the moment of inertia of the ring about a diameter 2.50×10−7kg⋅cm2, determine the angular speed of the ring as it passes through the second position. f the ring were free to rotate around any diameter, in what direction would the magnetic moment point when the ring is in a state of stable equilibrium? Enter the unit vector of that direction of the magnetic moment. Express your answer in terms of the unit vectors i^, j^, and k^.

μ⃗ /μ =

Answer 1