Calculating the Field strength of a magnet at a certain distance

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To calculate the magnetic field strength (B) of a permanent magnet at a certain distance, the inverse cube law is applicable for distances greater than five times the magnet's largest dimension. The equations provided, such as F = Bqv sin θ and F = BIL sin θ, can be used for measuring the field strength but come with practical challenges. The tools listed, including an ammeter and wire, suggest a method involving the force on a current-carrying wire to measure the field. Cutting a magnet in half does not simply halve its strength, as each piece remains a complete magnet with its own field. Understanding these principles is essential for accurately measuring magnetic field strength.
kaikalii
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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?
 
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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.
 
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