Dipole moment from electrostatic potential equation

[Iriasrol]

Homework Statement

Define the dipole moment starting from the elctrostatic potential equation for a multipole of order n step by step solution.

Relevant Equations

Potential equation V_n=\frac{P^{(n)}}{4\pi\epsilon_1r^{n+1}}P_n\cos{\theta}.

Final Dipole moment equation: P^{(n)}=\sum_{i=1}^Nq_id_i^n

Hello to everyone. The question or debate here is how you obtain the commonly known equation of dipole electric moment:

from the electrostatic potential equation for a multipole of order n:

I understand it is related with Dirac delta functions but a step by step solution might be helpful.Thank you very much

 

[kuruman]

Please read our guidelines here. We do not provide step-by-step solutions, but help you reach one after you show some effort at it.

 

[Iriasrol]

sounds awesome but I really do not know were to start :D

 

[kuruman]

sounds awesome but I really do not know were to start :D

You start by researching "multipole expansion" on the web. Choose a site that suits your level of understanding. Try to relate what you read to this particular problem. Then if you have a specific question, post it here and, if it is well posed, someone is likely to answer it. Makes sense, no? By the way, what is the definition of $d_i^n$ and what is $n$ for a dipole in the "commonly known" equation?

 

[Iriasrol]

For you to know it is the separation of the point charges constituting the n^th linear multipolar distribution on a multipolar moment of order n as its shown in this picture. And it is generalization for the COMMON dipole moment equation P=Qr. But sure you can start your research by looking for "dipole moment" on the web and choose a site that suits your level of understanding then you will find in a more complex definition the equation I wrote before...

Thanks for the help any way. If I am asking here its because I couldn't find exactly what I am looking for in a common basic electromagnetism book...