Calculating the Repelling Magnetic Force of Permanent Magnets

In this instructable you're going to learn how to calculate the repelling magnetic force of two permanent magnets. Note that the magnetic force depends on the distance between the two, so in the end we will not get a single number but an equation.

This is very easily done using the law of balaced forces. You need the following supplies:

• Magnets: you can use pretty much every two magnets that have the same shape
• some kind of (transparent) tube or rail where you can slide in your magnets. For example if you're testing cylindrical shaped magnets like me, you can use a straw. You can also roll up or fold some transparencys to fit your magnets
• a measuring tool like a ruler or caliper
• kitchen scale

First you need to weight your magnets. If you're using a kitchen scale, don't place them directly on the scale. Place them on a box to prevent affecting the scale's sensor.

If you've got two (or more) identical magnets, weight them together and divide your result by the number of magnets. The more the better because kitchen scales are not very accurate.

Note the weight for the calculation.

Place your tube on a table vertically (just hold it upright) and slide in your magnets from the top so that they're repelling each other. Depending on the weight and strength of the magnets there is a smaller or bigger gap between them. Measure and note the distance h as accurately as possible.

The upper (floating) magnet is experiencing the repelling force as well as gravitational force. As the lower magnet also experiences gravitational force, the gap between them is caused by the repelling force. That means that the repelling force of the magnets at the particular distance h equals the gravitational force of the upper (!) magnet:

Fm = Fg
=> Fm(h) = m * g

The potential energy of the upper magnet is calculated as follows: W = m * g * h

Since Energy is generally W = F * s, you can equalize the two equations and finally get:

W = F * s = m * g * h

=> F(s) = (m * g * h)/s

Just put in the measured mass (in kg), height (in m) and the location factor g = 9,81 kg/(m*s^2) and you get the repelling force in the pearticular distance s.