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 $$m=length/diameter$$

 

[sardar]

Hello there! Thank you for reaching out to the Physics Forums community for help with your experiment. I am happy to assist you with your question about the torque on a paramagnetic rod in a uniform magnetic field.

Firstly, let's define what a paramagnetic material is. A paramagnetic material is one that is attracted to a magnetic field, but does not retain any permanent magnetization when the field is removed. This is in contrast to ferromagnetic materials, which do retain magnetization after exposure to a magnetic field.

Now, to calculate the torque on a paramagnetic rod in a uniform magnetic field, we can use the equation:

τ = μ0χB^2Vsinθ

Where τ is the torque, μ0 is the permeability of free space, χ is the magnetic susceptibility of the material, B is the magnetic field strength, V is the volume of the rod, and θ is the angle between the direction of the magnetic field and the rod.

The magnetic susceptibility, χ, is a dimensionless quantity that describes the degree to which a material is attracted to a magnetic field. For paramagnetic materials, χ is positive and typically very small, indicating a weak attraction to the field.

I would also recommend checking out a book called "Introduction to Electrodynamics" by David J. Griffiths, which has a section on the torque on a paramagnetic material in a magnetic field.

I hope this helps you with your experiment. Best of luck!