Magnetic Power

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From Wikipedia:

Calculating the magnetic force

Calculating the attractive or repulsive force between two magnets is, in the general case, an extremely complex operation, as it depends on the shape, magnetization, orientation and separation of the magnets.

[edit] Force between two magnetic poles

Classically, the force between two magnetic poles is given by:^[13]

where

F is force (SI unit: newton) q_m1 and q_m2 are the magnitudes of magnetic poles (SI unit: ampere-meter) μ is the permeability of the intervening medium (SI unit: tesla meter per ampere, henry per meter or newton per ampere squared) r is the separation (SI unit: meter).

The pole description is useful to practising magneticians who design real-world magnets, but real magnets have a pole distribution more complex than a single north and south. Therefore, implementation of the pole idea is not simple. In some cases, one of the more complex formulae given below will be more useful.

[edit] Force between two nearby attracting surfaces of area A and equal but opposite magnetizing fields H ^[14]

where

A is the area of each surface, in m² H is their magnetizing field, in A/m. μ₀ is the permeability of space, which equals 4π×10⁻⁷ T·m/A [edit] Force between two bar magnets

The force between two identical cylindrical bar magnets placed end to end is given by:^[14]

where

B₀ is the magnetic flux density very close to each pole, in T, A is the area of each pole, in m², L is the length of each magnet, in m, R is the radius of each magnet, in m, and x is the separation between the two magnets, in m relates the flux density at the pole to the magnetization of the magnet.

Note that all these formulations are based on the Gilbert's model, which is usable in relatively great distances. In other models, (e.g., Ampère's model) predict a more complicated formulation, that some times, does not get solved analytical. Therefore, numerical methods may be used.

Source: Wikipedia.