Is the Quadrupole Moment Non-Zero?

[ispivack]

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.

 

[DrClaude]

What is the formula to calculate the quadrupole moment?

 

[kuruman]

If I did it right, the dipole moment has one non-zero component.