How to calculate the force between magnets?

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SUMMARY

This discussion focuses on calculating the force between magnets, specifically when determining the height required to achieve magnetic levitation between two like poles with a field strength of 1.5 Tesla. The formula for magnetic field strength, B = (μo * qm / 4π(r - l)²), is provided, where qm represents the pole strength and l is the half-length of the magnet. The conversation also explores the implications of using circular poles instead of point poles and suggests integrating the Maxwell stress tensor to calculate the total force on the magnets.

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  • Understanding of magnetic field strength and its calculation
  • Familiarity with the concept of pole strength in bar magnets
  • Knowledge of the Maxwell stress tensor in electromagnetism
  • Basic calculus for integrating differential forces
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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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