How to calculate the force between magnets?

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To calculate the force between magnets, the magnetic field strength at their surfaces is crucial, with an example given of 1.5 Tesla. For a top magnet supporting a weight of 1 Newton, the required height for hovering is sought. The force between bar magnets can be calculated using the formula F = Bqm, but this assumes point poles, raising questions about the impact of circular pole areas. Integrating the Maxwell stress tensor over the magnet's surface is suggested as a method to determine the total force, although it may require advanced mathematical understanding. The discussion emphasizes the complexity of calculating forces when dealing with non-point magnetic poles.
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For example at the surface of both magnets, the field strength is 1.5Tesla. Suppose the top magnet plus the weight it's supporting is 1 Newton, what is the height that I need to separate both magnets of like facing poles so that the top magnet hovers?
 
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ZecronTech said:
For example at the surface of both magnets, the field strength is 1.5Tesla. Suppose the top magnet plus the weight it's supporting is 1 Newton, what is the height that I need to separate both magnets of like facing poles so that the top magnet hovers?

Hint: The magnetic field B by a given pole of a bar magnet at a point (assume unit north pole) r cm away from its centre is given by,

B= (μoqm/4π(r-l)2)

Where qm is the pole strength of bar magnet. l is the "half length" of the bar magnet.

Hence classically the force between two poles of bar magnet is defined by F = Bqm. This formula is valid if the poles are mere points.
 
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sankalpmittal said:
Hence classically the force between two poles of bar magnet is defined by F = Bqm. This formula is valid if the poles are mere points.

So what if the poles aren't points like in the example that I gave. Suppose the magnets facing each other are circular. Would the difference between points and a circle area of 3cm2 be significant? If so, then how would you calculate it? (Forgive me if this post was already answered. I used the search function and came up with nothing related to this situation).
 
What about intregrating the differential forces between differential areas on each magnet? Would it work? Do you know what I mean?
 
ThomasO said:
What about intregrating the differential forces between differential areas on each magnet? Would it work? Do you know what I mean?

Yup I was also thinking the same, although I don't know how to do it. It's a bit above my math level.
 

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