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Equation of Motion: Example Problem

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A conducting loop of area A and total resistance R is suspended by a torsion spring of constant k in a uniform magnetic field B=B e_y. The loop is in the yz plane at equilibrium and can rotate about the z-axis with the moment of inertia I as shown in figure. The loop is displaced by a small angle Theta from equilibrium and released.
Assume the torsion spring is non-conducting and neglect self-inductance of the loop.

(a) What is the equation of motion for the loop in terms of the given parameters?

(b) Sketch the motion and label all the relevant time scales for the case when R is very large.

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