Calculating magnetic force between two bar magnets

[Ascendant78]

Homework Statement

Me and my physics II lab partner did a term project where we are looking to calculate the repulsive forces of two bar magnets on each other. We are lacking an equation that would let us calculate the force. All we did was have one magnet sit on a flat surface while we brought the other one closer to it in a parallel fashion until the magnetic force overcame the frictional force of the magnet. While we have all the pertinent data, we simply don't know what to do with that data to find the force at this point.

Homework Equations

We are unsure. We calculated the friction coefficient of the magnet on the surface it was repelled on top of, but we do not have a formula for the force between the two magnets.

The Attempt at a Solution

Here is all the information we have:
mass of magnet 1 (repelled) - 69g
mass of magnet 2 (repeller) - 68g
Distance at which the magnetic repulsion overcame the frictional force - 9mm
Friction coefficient (mu) of repelled magnet on top of aluminum surface - 0.277
Magnetic field at point of repulsion (repelled) - 0.439mT
Magnetic field at point of repulsion (repeller) - 0.439mT

They are both narrow, long bar magnets. I am thinking that their exact size will probably play a significant role here too, but I'm thinking I can guesstimate that or check tomorrow in class. However, if anyone has a relevant formula for magnetic forces that can work for us here, I'd greatly appreciate it.

 

[haruspex]

Forget about the magnetism for a moment. You have an object of known mass resting on a horizontal surface, and you know the coefficient of friction (static, I trust). What force is needed to overcome the friction?

 

[Ascendant78]

Forget about the magnetism for a moment. You have an object of known mass resting on a horizontal surface, and you know the coefficient of friction (static, I trust). What force is needed to overcome the friction?

We found the force to be 6.21x10^-4N based on that, but our professor also wanted us to try to find a way to calculate the force based on the the magnetic repulsion as well. That way, we could compare the two. He wasn't sure of a formula to do it off the top of his head, so he suggested we search the web. Nothing I found so far is feasible off the data we have nor off data we could obtain with our lab resources. Even if we found something that at least let us take a rough estimate, it would be better than nothing.

 

[haruspex]

We found the force to be 6.21x10^-4N based on that, but our professor also wanted us to try to find a way to calculate the force based on the the magnetic repulsion as well. That way, we could compare the two. He wasn't sure of a formula to do it off the top of his head, so he suggested we search the web. Nothing I found so far is feasible off the data we have nor off data we could obtain with our lab resources. Even if we found something that at least let us take a rough estimate, it would be better than nothing.

Take a look at http://en.wikipedia.org/wiki/Force_between_magnets#Force_between_two_bar_magnets. This is for magnets placed end-to-end, and uses the somewhat doubtful technique of treating the ends as magnetic monopoles. See if you can modify the terms in the second bracket to convert it to the parallel case. Don't forget to take into account vector addition.

 

[Ascendant78]

Take a look at http://en.wikipedia.org/wiki/Force_between_magnets#Force_between_two_bar_magnets. This is for magnets placed end-to-end, and uses the somewhat doubtful technique of treating the ends as magnetic monopoles. See if you can modify the terms in the second bracket to convert it to the parallel case. Don't forget to take into account vector addition.

Thank you. I did find this formula online a while back, but was hoping for something that didn't require magnetic flux density close to each of the poles. I'm thinking we will probably have to get back into the lab to find that as it seems to be the only equation that we could really work with at this point.