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Why does the N pole of a magnet do not attract with the same pole but the N pole of a magnet attracts with S pole?

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Suppose we start by considering electric charges. We all know that like electrical charges repel and unlike charges attract. The situation with magnets is more complicated because there are no such things as magnetic charges. The bar magnets that we are all familiar with are magnetic dipoles not magnetic charges.

If we switch back to electricity for a moment, electrical dipoles also exist and they behave like a pair of charges very close together:

Electric dipole

So the electric dipole has a positive end and a negative end. These are analogous to the north pole and south pole of a magnetic dipole. With this in mind it shoukld be obvious that two electric dipoles will attract if their unlike ends are pushed together and repel if their unlike ends are pushed together:

Dipole interaction

And the same argument applies to magnetic dipoles. Although magnetic charges don't exist a magnetic dipole behaves as if it has a north magnetic charge at one end and a south magnetic charge at the other. So they attract and repel in the same way that electric dipoles do.

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Various ways to think about it. Here's one;

The energy of the overall system is lower if the poles are closer. This creates a potential gradient (a hill), in which

  • external work must done, energy put in to separate the poles, but
  • energy is released if the poles are brought closer. Release energy is kinetic

Imagining an infinitesimal variation in relative position, any released kinetic energy in the direction converging the poles produces a positive feedback, i.e. more energy is released. Attraction is consequently observed.

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  • $\begingroup$ Of course one question leads to another; in this example it's why is the potential energy sloped that way - ultimately there must be some underlying assumptions for any model, but these should be simplified and minimised. That's hopefully a bit more helpful than just saying "because it is". $\endgroup$ – JMLCarter Jan 25 '17 at 13:38

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