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Suppose a bar magnet like so :


Do the two individual poles interact with each other ?

If yes then how do you explain it if no then how?

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There aren't two distinct poles. The battery is made up of lots of tiny magnets (e.g. iron atoms), and all those tiny magnets do indeed interact with other. The overall field of the magnet is the result of these interactions. The poles are just where the field leaves the end of the magnet.

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So they interact or not? – The-Ever-Kid Jul 26 '12 at 18:07

All the poles of the magnet (all the little poles in John Rennie's answer) interact with each other. The total magnetic energy is the field energy in the magnetic field everywhere in space:

$$ \int {1\over 2} B^2 d^dx $$

in appropriate units. Increases and decreases in this magnetic field energy also give you the energy changes when you bring two magnets together. The identification of the interaction potential energy with field energy removes any question of whether two objects interact--- the objects interact with the field, and the change in their energy as you change their configuration is the change in the field energy of this configuration. You don't have to do a pairwise sum over all poles to get the interaction energy.

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