# Calculating the force between a magnet and an electromagnet

## Main Question or Discussion Point

Hello. I would just like to begin by saying that I am very aware of the vast complexity of the subject of magnetism. Still, I have been hoping to find a way to get a basic idea of how much a magnet and an electromagnet are attracted or repelled by one another. I do not need highly perfect and precise values. Just something in the general ballpark.

I tried to use some of the simpler formulas listed in various Wikipedia articles. From http://en.wikipedia.org/wiki/Force_between_magnets#Force_between_two_magnetic_poles, I got this:

force (in newtons) = permeability (newton per ampere squared) * magnet (ampere-meter) * electromagnet (ampere-turn meter) / 4 * pi * separation (in meters) * separation (in meters)​

So, with one millimeter of separation (and a permeability of 1.2566e-6), this results in the force being 0.1 * the strength of the magnet * the strength of the electromagnet.

For the electromagnet, I used the equation shown here at http://en.wikipedia.org/wiki/Electromagnet#Force_between_electromagnets. Right below it, you can also see the equation I just previously mentioned.

ampere-turn meter = number of turns of wire * current (in amperes) * area of the core (meters squared) / thickness of the electromagnet (in meters)​

I made this little, flat, spiral coil for testing. It is seven turns of 30AWG (0.000254 meter thick) enameled magnet wire. I had a battery (size AA) that was outputting about 2 amps. Oh, and the air-core of the coil is about 2 millimeters in diameter.

So, 7 * 2 * 3.1415e-6 / 0.000254... My math gets me about 0.173 ampere-turn meter.

Now, all that is needed is the strength of the magnet. I have these little 0.25 inch neodymium-iron-boron cube magnets. Here are the specifications, as given by my source: http://www.rare-earth-magnets.com/p-26-nsn0606.aspx.

This is where I think I am messing up. I need to know the strength of one of these magnets in ampere-meters, but such does not appear to be explicitly listed. On some other site, I read that gauss-oersteds divided by gausses equals oersteds. And an oersted is 1000/4*pi ampere-meter.

So, 38000000 (the minimum listed in the specs) / 12800 (the maximum similarly listed)... 2968.75 oersteds (or just a little over 236000 ampere-meters).

The end result... I calculate a force of over 4000 newtons! That cannot be right... That would be over 400 kilograms-force! Yet, I could easily push my little electromagnet flat against one of my magnets, if I wanted. (And by no means do I have superhuman strength, either.)

Disappointed with the weak repulsion, I tried to measure what little force there was. Not having any good ways of doing so, I tried just sitting the little electromagnet on a digital kitchen scale and holding one of my magnets about a millimeter above it.

The scale reported about 2 to 3 grams. A crude measurement, no doubt. Still, it was all I could do.

So, the question: Where am I in err? As previously stated, I think it is something about the calculation of the strength of the magnet. Though, I will not disregard the possibility that my utilization of the various equations might also be incorrect.

One thing about my calculation for the strength of the magnet is that it does not appear to take into account the size of the magnet. And all of the N40 grade neodymium-iron-boron magnets seem to have the same megagauss-oersted (maximum energy density) and gauss (remanent flux density), regardless of their size.

The surface field, pull force, and such vary, but these two values seem to remain constant. Should I be taking into account the area or volume of my magnets? Am I otherwise completely off when it comes to determining the strength of one of these magnets?

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I just did a similar calculation,
using
permeability = 1.2e-6
mag_stength = 2000000 oesters = 159154943 Ampere/meters
turns = 7;
current = 2 amps
area = 1.58E-6 m^2
distance = 2mm gap
length of electromagnet = 3cm

gives me a force of 2900N.

A little more normal however that is still 290 kilos. dunno if this is still completely wrong. I dont have a neo magnet to test this