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

[klp_l123]

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 ...

 

[diazona]

Well what have you tried so far?

 

[klp_l123]

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 ...

 

[diazona]

Start with the formulas for the monopole "moment" (i.e. charge) and dipole moment. Do you know those?