# Calculating the flux density between two magnets

Summary:
Two rectangular magnets, each of 1 Tesla, are spaced 3cm apart, with their large areas facing each other - North facing South. How do I find the flux density at the point between them?
This is for an experiment to deflect a 28 SWG wire between two magnets, 3cm apart, by passing a current through it (example attached). The force on the wire is obviously F = BIL, but the wire will be passing at 1.5cm from each magnet so there will be some significant fall off of B and I can't assume B (in BIL) to be 2 Teslas. The magnets are 5cm × 1.9cm × 0.6cm and 1 Tesla each.

Many thanks,

Steve.

## Answers and Replies

gneill
Mentor
You're right that there will be falloff, and the flux density throughout the region between the magnet faces will not be uniform. You can predict the magnetic field for a rectangular magnet along its central axis fairly easily. See: this page. It's a commercial site with which I have no association or affiliation.

Elsewhere in the region between the magnets you'll probably have to resort to Finite Element Modelling software. There's one such mentioned on that website and they appear to be offering for free download.

Last edited:
SteveDavies
You're right that there will be falloff, and the flux density throughout the region between the magnet faces will not be uniform. You can predict the magnetic for a rectangular magnet along its central axis fairly easily. See: this page. It's a commercial site with which I have no association or affiliation.

Elsewhere in the region between the magnets you'll probably have to resort to Finite Element Modelling software. There's one such mentioned on that website and they appear to be offering for free download.

Thanks Gneill. Very useful!

Steve.

Summary:: Two rectangular magnets, each of 1 Tesla, are spaced 3cm apart, with their large areas facing each other - North facing South. How do I find the flux density at the point between them?

This is for an experiment to deflect a 28 SWG wire between two magnets, 3cm apart, by passing a current through it (example attached). The force on the wire is obviously F = BIL, but the wire will be passing at 1.5cm from each magnet so there will be some significant fall off of B and I can't assume B (in BIL) to be 2 Teslas. The magnets are 5cm × 1.9cm × 0.6cm and 1 Tesla each.

View attachment 256250

Many thanks,

Steve.

Two approaches, one would be to pass a known current through the wire and measure the force, then B=F/IL.

The second is the calculation method, and this is not as simple as it may seem. Permanent magnets are generally not offered as having x tesla. Fundamentally permanent magnets are a source of H or magneto motive force, the resultant B or flux density is determined by the reluctance of the magnetic circuit the magnet is in.

Now a permanent magnet will exhibit some flux density even in free space, since it has built in reluctance dependent on the shape of the magnet. It is this flux density that the linked page is calculating.

As soon as more magnets come into play, or you have a reluctance path other than air, these equations will not work. In this case you will have to at minimum estimate your magnetic circuit similar to this:

If you want to have the most force out of your wire in the case you have drawn, you'll want to add in magnetic path (ie iron) linking the backs of the magnets to each other so the only high reluctance path is through the air gap.

SteveDavies
Thanks essenmein.

The problem was that I couldn't get any movement from the wire. I think it's because at 28 SWG it was too rigid and heavy. I didn't have a horseshoe magnet available, so I was using separate magnets.

The Magnadur magnets are rated at 1 Tesla but according to supermagnete.de (I emailed them) the Tesla rating is measured at the centre of the magnet and at the surface it is always a lot less. Using their calculator, with the wire is at a distance of about 15mm from each magnet, it will have received a total field of about 0.1 Telsa.

So, over a length of 50mm (the length of the magnet) and at a current of 0.5A you get:

F = B I L

F = (0.1) (0.5) (0.05) = 0.0025 N

Which is equivalent to a mass of 0.25mg and is not enough to move the wire.

There are a couple of videos on YouTube though where they have managed to get this to work, but I think the wire they are using is a lot thinner - more like piano wire.

Thanks again for you suggestions,

Steve.

My preference, when all else fails, is more current.

If you build a little pulse switch thing with a fet and current limiting resistor to a power supply or something then you can put more amps through the wire, albeit for a shorter duration. I'd play with duration and some decent amps and see if you can get the wire to wiggle. Only reference I have is 110Adc will make the positive and negative wires move noticeably closer to each other when hanging in free air.

SteveDavies