loop axis A very small bar magnet with magnetic dipole moment m spins about its center on a vertical axle (2) at angular

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Loop Axis A Very Small Bar Magnet With Magnetic Dipole Moment M Spins About Its Center On A Vertical Axle 2 At Angular 1 (144.1 KiB) Viewed 63 times

loop axis A very small bar magnet with magnetic dipole moment m spins about its center on a vertical axle (2) at angular frequency w. At a distance d directly above the center of the magnet is a wire loop with area A whose axis (the normal to the area) is oriented horizontally (@, see figure; the loop lies in the y-z plane, the magnet spins in the x-y plane). At time t = -0, m is oriented parallel to the axis of the wire loop (i.e. m || ã; the figure shows a time t > 0). The loop is very small compared to the separation A« d- and the bar magnet is also small enough that it may be treated as a point dipole (the figure is not to scale). The loop has a total resistance R in comparison to which its inductance may be neglected (at frequency w) and you may furthermore assume wd « c, the speed of light. Hint: Recall that the first nonvanishing term in the multipole expansion of the magnetic vector potential is given by d m До т Хr A= 47 r2 (1) (a) What is the current in the wire loop as a function of time? (b) The wire's current creates a magnetic field at the magnet. What is the resulting torque on the magnet as a function of time? (c) What is the time-averaged power which must be supplied to keep the magnet spinning at constant frequency w?