How to calculate the force between magnets?

[ZecronTech]

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?

 

[sankalpmittal]

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= (μ_oq_m/4π(r-l)²)

Where q_m 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 = Bq_m. This formula is valid if the poles are mere points.

 

[ZecronTech]

Hence classically the force between two poles of bar magnet is defined by F = Bq_m. 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).

 

[ThomasO]

What about intregrating the differential forces between differential areas on each magnet? Would it work? Do you know what I mean?

 

[ZecronTech]

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.

 

[mikeph]

The general way is to integrate the Maxwell stress tensor over the surface of the object you're interested in, and that will give you the total force on the object.

http://en.wikipedia.org/wiki/Maxwell_stress_tensor#Magnetism_only