How Does Cylindrical Symmetry Affect the Quadrupole Moment Matrix?

Josephk1508
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Homework Statement




Show that, if a charge distribution  has cylindrical symmetry, then knowing the value
of Qzz allows you to determine the entire quadrupole moment matrix.

Homework Equations



Tr Q=0, ie Qxx+Qyy+Qzz=0

The Attempt at a Solution



Because of the cylindrical symmetry, the charge density changes as a function of ρ, where ρ=(x^2+y^2)^1/2. Then I don't really know where to go from there.
 
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I have now worked out all values for the quadrupole matrix, I just need to calculate what Qzz is. If anyone can help that would be really useful. Also I realized I made a mistake above, cylinrical symmetry means that it is dependent only z only.
 

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