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

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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 B⃗ =(1.15×10−2T)(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
is 2.50×10−7kg⋅m2, determine the angular speed of the
ring as it passes through the second position.