Dipole and Quadrupole moments and axial symmetry

[lapantufla]

Homework Statement

Show that if the charge (or current) distribution has axial symmetry then the electric (or magnetic) dipole moment is null.
Show that the quadrupole moments Qij with i different from j are null under the same conditions.

Relevant Equations

Electric Dipole Moment Equation.
Magnetic Dipole Moment Equation.
Quadrupole Moment Equation.

Hello, I would like to find a mathematical demonstration of this problem. While I have always used it, I could never prove it. Given a charge or current distribution with axial symmetry the electric and magnetic dipole moment are null:

(electric dipole moment)

(magnetic dipole moment)and that the elements outside the diagonal of the quadrupole moment are also canceled:

(Quadrupole moment)From already thank you very much. (excuse my English, I use a translator).

 

[DrClaude]

We can't do your work for you. Start the problem, post to explain where you get stuck, and you will get some help.

 

[BvU]

Hello lapantufla, !

Please read the guidelines -- we require an effort from you

Homework Statement:: Show that if the charge (or current) distribution has axial symmetry then the electric (or magnetic) dipole moment is null.

Seems to me something was lost in translation: even the simplest dipole example has axial symmetry.

re lapantufla: does it have a meaning in your language ?