Modeling the interaction of a slowly rotating hollow conducting sphere in a magnetic field provided an understanding of the dynamics of orbiting space objects moving through the Earth's magnetic field. This analysis, performed in the late 1950s and limited to uniform magnetic fields, was innovative and acknowledged the pioneers who first observed rotary magnetism, in particular, the seminal work of Hertz in 1880. Now, there is interest in using a magnetic field produced by one space object to stop the spin of a second object so that docking can occur. In this paper, we consider, yet again, the interaction of a rotating hollow sphere in a magnetic field. We show that the predicted results can be tested experimentally, making this an interesting advanced student project. This analysis also sheds light on a rich set of previously unaddressed behaviors involving eddy currents.
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The terminology, “
advection current
” isn't prominent in literature, but the adjective “advection” seems fitting to describe this current. There is an apparent current due to the motion of the charges as they are carried around by the turning of the sphere, similar to the way a floating leaf is carried along by a river. There is no Ohmic loss, yet the charges are in motion.22.
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Wikipedia contributors
, Associated Legendre polynomials, Wikipedia, The Free Encyclopedia, May 18, 2015
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