# Calculating magnetic force between two bar magnets

**1. The problem statement, all variables and given/known data**

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.

**2. Relevant 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.

**3. 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.

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Solution: Static friction u should be used; for Al it’s 0.42

When the 2nd magnet is moved toward the 1st at x = 9 mm,

Fmag (at x = 9mm) = 2 * u (static) * F(normal) = u*m1*g = 0.42 * 0.069 * 9.80665 = 0.56839 newtons

The reason it’s 2 * u*m1*g is because m2 repulses m1 and m2 repulses m1 repulses m2.