How Do Charge Distributions Affect Monopole, Dipole, and Quadrupole Moments?

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Homework Help Overview

The discussion revolves around the effects of charge distributions on monopole, dipole, and quadrupole moments, specifically in the context of a point charge and a surrounding charge distribution with cylindrical symmetry. The original poster seeks assistance in demonstrating the properties of these moments for prolate and oblate charge distributions.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are examining the relationships between charge distributions and their corresponding moments, questioning how the monopole and dipole moments can be zero while the quadrupole moment varies in sign. The original poster expresses uncertainty about the conditions leading to the zero values of the monopole and dipole moments.

Discussion Status

The discussion is in an exploratory phase, with participants seeking to clarify fundamental concepts and relationships. Some guidance has been offered regarding the formulas for monopole and dipole moments, but there is no explicit consensus on the reasoning behind the zero values of these moments.

Contextual Notes

The problem involves specific charge distributions (prolate and oblate) and their implications for the moments, which may require further clarification or assumptions about the nature of these distributions.

klp_l123
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a point charge +Q is placed at the origin and a charge -Q is smeared around the origin maintaining cylindrical symmetry around the Z axis.Show that (i) when the charge distribution is prolate(egg-shaped),the monopole and dipole moments are zero but the quadrupole moment Q is positive; (ii) when the charge distribution is oblate(pizza-shaped),the monopole and dipole moments are again zero but the quadrupole moment is negative. please help me solving this problem ...
 
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Well what have you tried so far?
 
by the quadropole relation what we know, i can say about the +ve and -ve sign of Q ... but i cannot understand about monopole & dipole term- how they are goinh to zero ...
 
Start with the formulas for the monopole "moment" (i.e. charge) and dipole moment. Do you know those?
 

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