# Permanent magnet B field equation

1. Jan 27, 2007

### lincsimp

hey
how would I go about calculating the B field of a bar magnet?

I've already managed to calculate the electric field between two charged particles etc and draw that, but I just can't see where to start with this one as its not just a point at north and south but a whole load of atoms working together.

If anyone could point me to some equations that would be good or just provide some ideas about where to start...

(btw this is not a hw q, just something I was wondering)

thank you!

2. Jan 27, 2007

### Hootenanny

Staff Emeritus
Welcome to the forums,

Start here: http://instruct.tri-c.edu/fgram/web/Mdipole.htm [Broken]

Last edited by a moderator: May 2, 2017
3. Jan 27, 2007

### lincsimp

Thank you hootenanny; that appears to be what I was looking for! I'll be back if/when any problems arise... :)

4. Jan 27, 2007

### Meir Achuz

Don't trust that website. It starts:
"A bar magnet is a magnetic dipole, and its field varies in the space around the magnet in the same way as the electric field varies around an electric dipole. So we can use the results of the E calculations to find the magnetic field B and forces between magnets."
But, that is only a reasonable approximation when two bar magents are far apart. For magnets at any distance, you can treat the end surface of each bar magnet as a uniformly charged disk. Then make reasonable approximations from that model, depending on the distance and orientation of the magnets.

Last edited by a moderator: May 2, 2017
5. Jan 27, 2007

### arunma

Interesting question. I vaguely remember doing this in E&M. Do I remember incorrectly, or doesn't a bar magnet have the same field as a stack of AmpĂ¨re dipoles (i.e. a solenoid)?

6. Jan 28, 2007

### lincsimp

hmmm... so it looks as though this is something I'll have to derive for myself. I think I'm going to treat each end as a uniformly charged disk...

http://www.richmond.edu/~ggilfoyl/genphys/132/102solutions/Ch26/EOC_Solution_26_15.pdf [Broken]
https://www.physicsforums.com/archive/index.php/t-123091.html
http://ocw.mit.edu/NR/rdonlyres/Physics/8-022Fall-2004/9A6AC77A-6CA0-431A-BA90-9FBA4A5C7027/0/lecture2.pdf [Broken]

I feel pretty close now, but I guess I'm going to need to refresh my differential equations and learn Gauss's law. If anyone's done a course on EMFs it be great if you could give some suggestions/etc., but otherwise it looks at though I'll have to figure it myself.

Thank you :)

John

Last edited by a moderator: May 2, 2017
7. Jan 29, 2007

### lincsimp

hi again

I decided to give up with the complicated integral's (although they would hae been fun!) for now and decided to use a large array of point charges in layers alternating +ve,-ve,+ve.... (red = +ve, blue = -ve)

An Euler iteration with Coulomb's Law got me that image (and I could have had them coming back in the top if I'd waited). Does it look right? How could I speed it up? What would I need to change to make them look more like "elephant ears"?

thanks

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