Paramagnetic rod in a uniform magnetic field

[little]

Hello Physics Forums. I've read the forum on and off for a while and have always found that the folks here have given such thorough answers that I've had nothing more to contribute! :) But I finally have the need to ask a question.

I work in a physics lab and we are trying to determine the effects of magnetic fields on an aluminum torsion balance. Nominally, the effects are very small because it is paramagnetic, but this is an extremely sensitive device so we believe we need to do all the calculations to make sure we aren't having problems with magnetic fields.

Specifically, when a freely suspended rod (magnetized, ferromagnetic or paramagnetic) is placed in a uniform magnetic field, a torque results that moves the rod in line with the field. I've having the darnedest time finding a formula for this torque for anything other than a magnet. Can anyone help me out with a paramagnetic material - or even suggest a book? I've scoured the 4 or 5 books in the lab that might contain such an equation but haven't found anything.

 

[little]

I have access to that journal - would you provide a more thorough citation so I can find the article?

I also just found an interesting reference. I had mainly been focusing on books that dealt with theory, but I found one on an application that I hadn't considered. Namely, it's dealing with the repercussions of foreign objects in the body when undergoing magnetic resonance procedures! A needle is precisely the sort of thing they would be concerned about. However, the equation they have doesn't have appear to have the proper units at first glance. Unfortunately, the preceding page is missing in google books so I suspect it's the assignment of the 'D' variables (I was using simple distance measures of the axes of the ellipse). Any other thoughts on this equation?

(holy moly, I'm dense - I can't get latex to work out right)

T=[(chi^2*V*B^2)/mu0]*(Da-Dr)*cos(theta)*sin(theta)


The units come out to Nm^2 if you assume the 'D's are lengths. Elsewhere in the text it defines a needle like object as Da<<Dr.

 

[little]

Sorry of the double post...but...

I googled real quick and found an article about it in the American Journal of Physics, Volume 19. It sounded worthwhile, but I couldn't find the full article anywhere. It still being studied pretty closely, so I don't know if any books will have anything other than the magnetic formula.

Hope this helps.

Looking into this, volume 19 was published in 1951! Do you have any other reason for believing this is still being studied closely?And I've finally realized that my preview does not properly show latex...arg. Here's the equation:

T=\frac{\chi^2VB^2}{\mu_0}(D_a-D_r)cos(\theta)sin(\theta)

 

[little]

In case anyone has been watching this thread with bated breath, I've discovered the issue.

The D terms are 'demagnetization factors'. For the case of a long skinny object Da<<Dr. And

D_r=\frac{4\pi}{m^2}(ln(2m)-1) where m=length/diameter