Is magnetism more concentrated at the more pointed pole?

  • Thread starter slakedlime
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  • #1
slakedlime
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There's a principle that the electric field is stronger/more intense at the most pointed parts of a charged, non-uniform conductor.

Does this principle also apply to magnets? I.e. if we have a non-uniform magnet, is the magnetism density (sorry for the lack of a more scientific word) greater at the pointed parts? I suppose, however, the total intensity of the north pole will equal that of the south pole.

Just out of curiosity, suppose we have the following non-uniform magnet. Would its magnetic field resemble that of a similar charged conductor (except for the fact that it has a magnetic, not electric field)?

magnet.jpg
 

Answers and Replies

  • #2
slakedlime
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Diagram charge distribution on a similarly-shaped conductor:
conductor.jpg
 
  • #3
vanesch
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The simple answer is yes. Lines of the magnetic induction (B) - often called the magnetic field, although strictly speaking that's different (H) are in the static case we address here, closed loops. As you say, ideally, there are as many that enter the magnet on one side as leave on the other, so if the place where they live is more pointed, there are more of them per unit of surface, which means that the magnetic induction flux density is higher.
BUT: as where conductors and dielectrics are hugely different in their conduction (the resistivity of insulators is billions of billions of times higher than the resistivity of conductors), this distinction is much less so for magnetic permeability. There's at most a factor of a few thousand between the "magnetic conductivity" of a "magnetic material" such as ferrite and an "a-magnetic material" such as plastic or air (I'm being somewhat coarse here). As such, magnetic field lines "leak out all the time", and it is less evident to make them concentrate "on the tip of the magnet". But nevertheless, there will be some effect of concentration.
 

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