MadSci Network: Astronomy
Query:

Re: How do I convert magnetic susceptibility into kilograms of force?

Date: Thu Jan 4 21:41:01 2001
Posted By: Steve Furlanetto, Grad student, Astronomy, Harvard-Smithsonian Center for Astrophysics
Area of science: Astronomy
ID: 977598712.As
Message:

The magnetic susceptibility, s, is defined by M = sH, where M is the magnetic dipole moment per unit volume of the material and H is essentially the part of the magnetic field that is independent of the material (bold type means that the quantities are vectors). Basically, this equation means that in materials for which one can define a magnetic susceptibility, the induced magnetic dipole is simply proportional to the external field.

The equation for the force on an infinitesimal magnetic dipole m in a magnetic field is F = grad (m.B), where grad is the gradient operator (a vector derivative) and the dot is the vector dot product. This formula strictly only applies to infinitesimal dipoles, although it will be pretty accurate for any object whose size is small compared to the length scale over which the magnetic field varies (which may be quite small near a neutron star!). Otherwise, you will get magnetic "tides" because the force on different parts of the object will be different! Gravitational tides are quite strong near objects like black holes and neutron stars, and, in your scenario, the magnetic tides could be very important as well.

To really get a good grip on this issue, I would recommend that you take a look at an electricity and magnetism textbook. The best advanced undergraduate level textbook is Griffiths, Introduction to Electrodynamics, which has a whole chapter on magnetic fields in matter.

Something to keep in mind is that the gravitational forces near neutron stars are huge! I would expect them to dominate the weak magnetic forces on paramagnetic and diamagnetic objects in almost all cases. So if you are going for realism, the magnetic forces may turn out to be unimportant.

Good luck with the stories!


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