What Volume Is Integrated Over for Dipole Moment in Griffiths' Electrodynamics?

[Wheelwalker]

In "An Introduction to Electrodynamics", Griffiths gives the following equation for the dipole moment: $p=\int r' \rho(r') d\tau'$. My question is, in general, what volume am I integrating over? It seems a bit arbitrary to me. I assume I'm integrating over whatever volume is enclosing the charge density $\rho(r')$?

 

[TSny]

You are summing over all elements of volume $\small d\tau'$ in all of space. However, there is no need to integrate over those parts of space where the integrand is zero. So, you are correct - you only need to integrate over regions where there is some nonzero charge density.

 

[Wheelwalker]

That makes sense to me. Thanks!