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My son asked me this question and I was stumped - my intuition says that is the south pole was strong enough the attraction between the north and south poles would outweigh the repulsion between the two north poles - but how strong would the south pole need to be in this case?

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The geometry behind the "inserting" isn't quite clear. Also, the electrostatic and magnetostatic interactions are pairwise. The force acting on A is the sum of forces from all other objects, so the force between A and B (a contribution to the force acting on A; or B) isn't affected by any additional C. C itself may exert forces on A,B but these are different forces. These are reasons why your questions sounds incomprehensible to me. – Luboš Motl Jan 11 '12 at 15:51
up vote 2 down vote accepted

Assuming long skinny solenoidal magnets, so that their ends look like point magnetic sources, the force between two poles is $M1M2/r^2$, just like electrostatics, with pole density replacing charge density, where $M1$,$M2$ is the strength of the pole, and $r$ is the separation between the poles.

So you have three poles at position -A,0,A with magnitudes in the ratio 1:-1/4:1 respectively, the total repulsive force on the left-most one from the rightmost one is exactly balanced by the force from the middle one. Twice the distance means 1/4 the force.

For real magnets, you will usually not be able to get the other poles far enough away to have what looks like a monopole source. Then the answer depends on the geometry, but the above is a rough guide.

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