Electromagnetism - Quadrupole , Octupole

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Homework Help Overview

The discussion revolves around calculating the electric fields of quadrupole and octupole configurations in spherical coordinates, focusing on the application of multipole expansions and potential theory.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants raise questions about the specific arrangements and properties of the charge distributions involved, such as charge equality and geometric configuration. There is also mention of using multipole expansion techniques and references to relevant literature for further guidance.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the problem setup. Some guidance has been offered regarding the use of multipole expansions, but there is no explicit consensus on the specifics of the charge arrangements or the necessary assumptions.

Contextual Notes

There are indications of missing information regarding the arrangement of charges, such as whether they are equal and how they are positioned, which may affect the calculations and interpretations of the electric fields.

syracuse1234
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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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