Compass Needle in Uniform and Rotating Magnetic Fields

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A compass needle undergoes forced oscillations under the influence of a uniform magnetic field and a rotating magnetic field
with angular velocity
(black arrow). The compass needle has a moment of inertia
, a friction constant
, and a magnetic moment ℳ. This is a simple example of a system that shows chaotic motion. In a real experiment it is impossible to repeat a particular motion from initial conditions
and
because the system is chaotic.
Contributed by: Enrique Zeleny (March 2011)
Open content licensed under CC BY-NC-SA
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Details
The differential equation to solve is .
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