How do I calculate the quadrupole moment for three point charges on the z-axis?

[fizikx]

quadrupole moment??

The problem basically states that there are three point charges: q, -2q, q, placed along the z-axis at: a, 0, -a. The problem asks to find the monopole moment, dipole moment and quadrupole moment. I've been able to get the first to, but I have no idea how to go about getting the quadrupole moment. Tge prof never really explained it, so can someone please explain what the quadrupole moment matrix is...

 

[siddharth]

The problem basically states that there are three point charges: q, -2q, q, placed along the z-axis at: a, 0, -a. The problem asks to find the monopole moment, dipole moment and quadrupole moment. I've been able to get the first to, but I have no idea how to go about getting the quadrupole moment. Tge prof never really explained it, so can someone please explain what the quadrupole moment matrix is...

These links may help

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elequad.html#c2
http://orca.phys.uvic.ca/~tatum/elmag/em3.pdf - pdf file

 

[Meir Achuz]

For a collection of point charges, the quadrupole moment is defined as
Q=Sum_i{q_i r_i^2 [3cos^2(theta_i)-1]/2}.
For your case, theta is either 0 or 180.

 

[fizikx]

Thank you both:):)