A circular ring with area 4.45 cm2 is carrying a current of 12.5A. The ring, initially at rest, is immersed in a region of uniformmagnetic field given by B⃗ =(1.25×10−2T)(12i^+3j^−4k^). The ring ispositioned initially such that its magnetic moment orientation isgiven by μ⃗ i=μ(−0.8i^+0.6j^), where μ is the (positive) magnitudeof the magnetic moment. (a) Find the initial magnetic torque on thering. (b) The ring (which is free to rotate around one diameter) isreleased and turns through an angle of 90.0∘, at which point itsmagnetic moment orientation is given by μ⃗ f=−μk^. Determine thedecrease in potential energy. (c) If the moment of inertia of thering about a diameter 2.50×10−7kg⋅cm2, determine the angular speedof the ring as it passes through the second position. f the ringwere free to rotate around any diameter, in what direction wouldthe magnetic moment point when the ring is in a state of stableequilibrium? Enter the unit vector of that direction of themagnetic moment. Express your answer in terms of the unit vectorsi^, j^, and k^.
μ⃗ /μ =
