magnetic fields

[Michael Crofton <croft001@maroon.tc.umn.edu>]

I am a high school physics teacher and one of my former students posed
the following question to me.  I am having trouble developing a concise
answer to his question.  Any help out there?

Thank you,
Michael Crofton

> If we consider a bar magnet (or equivalently a compass needle), the
> textbook states that the direction of the magnetic dipole moment is >from the south pole to the north pole.

> Suppose we have a very large horseshoe magnet, and in the space between
> the ends, the field is approximately uniform (we ignore any
> "fringing").  The direction of the H and B fields is from the north >pole to the south pole.

> {Note: The Materials Science text uses H to denote magnetic field
> strength, and B to denote magnetic induction or magnetic flux density: >B = (permeability)(H).}

> Suppose I have a solid material where each atom has a permanent dipole
> moment due to incomplete cancellation of electron spin and/or orbital
> magnetic moments (that is, a paramagnetic material).

> I place said paramagnetic material between the poles of the magnet.  >The magnetic dipole moments then align with the B field within the
> material.  But magnetic dipole moments point from S to N of the >magnetic dipole, while the B field direction is from the N to the S >pole of that large horseshoe magnet creating the B field.  Therefore >the "north" ends of the atoms of the paramagnetic material are facing >the south pole of the horseshoe magnet, and the "south" ends of the >atoms of the paramagnetic material are facing the "north" end of the >magnet, in accordance with opposite polarities attracting.  

> So the dipole moments of the atoms point in the same direction as the
> applied B field. But, the magnetic fields created by the atomic dipoles
> point in the opposite direction as their dipole moment: the dipole
> moment is from S to N; the field they create is directed from N to S. 
> Since the magnetic fields created by the atomic dipoles point in the
> opposite (antiparallel) direction as their dipole moment, they also
> point in the opposite direction as the external field of the horseshoe
> magnet.  I would reason, therefore, that the field created by the
> dipoles in the paramagnetic material COUNTERACTS the field of the
> horseshoe magnet.  Similarly, the E field of the electronic dipoles in >a dielectric material between the plates of a capacitor is in the >opposite direction (and counteracts) the E field applied to the >dielectric medium by virtue of the difference in potential between the >capacitor plates.

> So while I conclude that the dipoles' fields COUNTERACT the applied
> field, the textbook says, "Inasmuch as the dipoles align with the
> external field, they ENHANCE it, giving rise to a relative permeability
> that is greater than unity."

> Where have I gone wrong in my reasoning?  What the textbook says would
> be like saying with reference to a capacitor with dielectric, "Inasmuch
> as the dielectric's electronic dipoles align with the external field,
> they enhance it," which is clearly wrong.  But it is true that the
> relative permeability of paramagnetic materials is greater than unity,
> so I must be wrong.