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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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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