Calculating the Field strength of a magnet at a certain distance

[kaikalii]

Is there a way to calculate the magnetic field strength, B, of a magnet (permanent magnet, not an electromagnet) at a certain distance? I assume it follows the inverse square law, but other than that, I do not know what to do.

Tools I have available:

• permanent magnet
• ammeter/voltmeter
• wire
• batteries
• spring scale
• ruler

I am aware of the equations: F=8.99*10⁹q₁q₂/r², F=qVB(sinθ), and F=BIL(sinθ), but I do not know how I would use those to calculate the field strength with just the tools listed above.

Also, if you were to cut a magnet in half, would that half the strength of the magnetic field? Does every type of permanent magnet material have some kind of Tesla per meter² per kilogram constant?

 

[Philip Wood]

Do you really want to calculate the field? Your inclusion of a list of tools suggests that you want to measure it.

The equations you have listed won't help you calculate the field strength at a distance from the magnet, though $F = Bqv sin \theta$ is the basis of the Hall probe for measuring the field strength, and $F = BIL sin \theta$ could also be used - with considerable practical difficulties - for this purpose. Your list of tools seems to be chosen with this last method (measuring the force due to the field on a current-carrying wire) in mind.

Close to the magnet the field will vary in a complicated way, partly dependent on the magnet's shape. Far from the magnet (say > 5 times the magnet's greatest dimension. e.g. length) I would expect the field to fall off roughly as the inverse cube of the distance from the centre of the magnet.