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Would one consider the following to be a monopole, or a dipole?

by Gravitas
Tags: dipole, monopole, polarities, sphere
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Gravitas
#1
Aug12-11, 12:02 AM
P: 2
I hope that I have chosen the correct thread and that this belongs here.
I understand the concept of a dipole, where you have opposite polarities at each end of a lineal object, i.e. a magnet. My question concerns the case of a sphere, where the outer surface is one polarity and the center is another, rather than a sphere that is merely 'half and half'. Considering that one pole is completely surrounded (enclosed) by the other pole, does this still count as a dipole, or does it now qualify as a monopole. Also, what are the criteria that would allow one to distinguish between different types (arrangements) of poles, to qualify as mono- vs di-? Thanks in advance for your help in enlightening me on this point. Gravitas
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torquil
#2
Aug12-11, 06:11 AM
P: 641
Quote Quote by Gravitas View Post
I hope that I have chosen the correct thread and that this belongs here.
I understand the concept of a dipole, where you have opposite polarities at each end of a lineal object, i.e. a magnet. My question concerns the case of a sphere, where the outer surface is one polarity and the center is another, rather than a sphere that is merely 'half and half'. Considering that one pole is completely surrounded (enclosed) by the other pole, does this still count as a dipole, or does it now qualify as a monopole. Also, what are the criteria that would allow one to distinguish between different types (arrangements) of poles, to qualify as mono- vs di-? Thanks in advance for your help in enlightening me on this point. Gravitas
Since it is completely spherically symmetric, it is a monopole.

The definition has to do with so-called spherical harmonic expansions of e.g. the angular dependency of the scalar potential that surrounds the object, due to the charges it contains. Since your object contains charge densities of some kind, it is surrounded by such a field. Since the charge density is spherically symmetric, the spherical harmonic expansion of the angular dependent part of this field will contain only the lowest order spherical harmonic. Therefore, this is called a monopole field. If the charge is electric, your object is called an electric monopole.


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