Is the Quadrupole Moment Non-Zero?

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SUMMARY

The discussion centers on the evaluation of the quadrupole moment in physics, specifically in the context of multipole expansions. The participant asserts that both the monopole and dipole moments are zero, while indicating that the dipole moment has one non-zero component. The inquiry focuses on the formula required to calculate the quadrupole moment, highlighting a gap in understanding regarding its evaluation.

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Homework Statement
Given ##\rho=(k/r)sin(\theta)cos(\phi)## for a sphere of radius R, find the lowest non-vanishing multipole moment.
Relevant Equations
General multipole expansion equation, as well as spherical harmonics (I think).
I have been throwing everything I can at this. I believe that both the monopole and dipole are zero, but I have no clue as to how to evaluate the quadrupole moment.
 
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What is the formula to calculate the quadrupole moment?
 
If I did it right, the dipole moment has one non-zero component.
 
Last edited:

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