# Coulomb's Law/Universal Gravitation for Magnets

1. Mar 15, 2013

### DFTBA

Hey, everyone, I'm new here. I signed up to get an equation that I would really like to find, but I've been searching for a few days and haven't found anything that helped. What I'm wondering is how to find the force between two magnets. Once I have that equation, I'll ask another one that I want to combine with it. Thanks for help from anyone out there willing to stick out a helping hand!

2. Mar 15, 2013

### Staff: Mentor

I googled Force Between Two Magnets, and got lots of helpful hits. You could try the same search to see if it gives you what you need. Here is one of the hits for a force calculator:

http://www.kjmagnetics.com/calculator.asp

BTW, your thread title is worrisome. What in the world do you mean by it?

3. Mar 15, 2013

### ModusPwnd

My first thought was that he wants something like this, F = qv x B

DFTBA, is this familiar?

4. Mar 15, 2013

### DFTBA

I mean that there is an equation for attraction between charges: Coulomb's law. There is an equation for attraction between masses: universal gravitation. I'm asking for the same idea, but with magnets.

That equation is not familiar to me. Most of my research does not involve magnetism. However, I don't understand how that could work. Stationary magnets still attract, but the equation seems to say a zero velocity would yield a non-existent force.

5. Mar 15, 2013

### ModusPwnd

The 'v' is the velocity of the charge 'q'. Magnets are complicated collections of lots of charges. The equation is a vector equation with the 'x' being a cross product. Note that when you combine it with the coulomb force you get the "lorentz force", F= qE + qv x B

http://en.wikipedia.org/wiki/Lorentz_force
http://hyperphysics.phy-astr.gsu.edu/%E2%80%8Chbase/magnetic/magfor.html [Broken]

Last edited by a moderator: May 6, 2017
6. Mar 15, 2013

### DFTBA

Okay, this seems to be on the right track. But how do I put two magnets into the equation?

7. Mar 15, 2013

### ModusPwnd

That is a lot more complicated. Magnets are bulk materials made up of many particles that have charge and "magnetic moments" (link). The properties are fundamentally quantum mechanical and quite complex.

I think your best bet is to start with the links I gave you for understanding the basic theory behind the magnetic force. I would use the link provided by berkeman to find the force of a real physical magnet. (or an experiment of your own)

This is one area where it take a lot of work to go from the basic theory to a real prediction.

8. Mar 16, 2013

### Astronuc

Staff Emeritus
I believe that one is looking for the mathematics describing dipole-dipole interactions.

Some simple geometries: http://en.wikipedia.org/wiki/Force_between_magnets#Calculating_the_magnetic_force

It becomes more complex with the goemeteries of the sources of the magnetic fields.
http://en.wikipedia.org/wiki/Magnetic_dipole–dipole_interaction

http://geophysics.ou.edu/solid_earth/notes/mag_basic/mag_basic.html [Broken]

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

Last edited by a moderator: May 6, 2017
9. Mar 16, 2013

### Staff: Mentor

Here are some reasons why the situation is so complicated:

1. The magnetic field around a magnet isn't spherically symmetric like (at least approximately) the gravitational field around the earth or a planet. So the force depends not only on distance, but also on the relative orientation of the magnets.

2. The general mathematical form is different depending on whether you're close to the magnet, relative to its size (the "near field") or far away from it ("far field"). If you're very close to the magnet, the field is influenced by the detailed shape of the magnet itself. Consider a cylindrical bar magnet, 1 cm in diameter and 5 cm long. It makes a difference whether you're 1 cm from it, or 10 cm, or 1 m, or 10 m. I think at 10 m you'd definitely be in the "far field" zone. At 1 m it probably depends on how precise you want to be. 10 cm is probably "near field".

The formula given by Astronuc's link

http://en.wikipedia.org/wiki/Magnetic_dipole–dipole_interaction

would apply to the "far field" situation.

Last edited: Mar 16, 2013