> What properties would a magnet have if it had negative permeability? I
> have read that certain materials have this property at microwave
> frequencies - but what effect does it have on magnetism?
From the relationship between the magnetic field and magnetic induction
(B = uH, where u = mu, the permeabiltiy), having a negative permeability
just means the magnetic field within ponderable matter would point the
opposite direction to the field in free space.
The permeability (and permittivity) can take complex values, and also
vary with frequency. The negative portion refers to, IIRC, the real
component. The metamaterials you may have read about are interesting
because *both* the permittivity and permeability are negative, and only
over a small frequency range. Also, the absorption is high in the
region of negative refractive index.
http://en.wikipedia.org/wiki/Metamaterial

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Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University