Electromagnetism - Quadrupole , Octupole

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The discussion focuses on calculating the electric fields of quadrupoles and octupoles in spherical coordinates, emphasizing the need for clarity on charge arrangement and distances. Participants highlight the importance of specifying whether the charges are equal, their distances, and their geometric configuration. The multipole expansion is recommended for potential calculations, particularly using Legendre polynomials for axially symmetric charge distributions, and spherical harmonics for non-symmetric cases. A specific example is provided, detailing a configuration of positive and negative charges leading to a potential expression. The conversation underscores the complexity of multipole arrangements in electromagnetism.
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1.Calculate the electric field of a quadrupole in spherical coordinates.

2.Calculate the electric field of a octupole in spherical coordinates.
 
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There seems to be missing some information here. How exactly are those multi-poles arranged? equal charges? equal distances? Regular polygons? "a quadupole" or "an octopole" are very wide terms indeed
 
syracuse1234 said:
1.Calculate the electric field of a quadrupole in spherical coordinates.

2.Calculate the electric field of a octupole in spherical coordinates.

Use the multipole expansion for the potential in terms of Legendre polynomials for the case of an axially symmetric chargel distribution. If itr is not axially slymmetric, you need the spherical harmonic expansion.
 
Also see Boas (Math Methods) Ch. 12 sect.5 ex. 1 for future reference. Solution if You have 2 +ve charges Q at +/- "a" on y-axis and 2 -ve charges Q at +/- "a" on x-axis is V=\frac{-3Qa^{2}cos(2\theta)}{4\pi\epsilon_{0}r^{3}}
 

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