This one comes from the Landau & Lifschitz series, where they love to make you figure out what they did :).
This is from Chapter 2, section 6 of the Electrodynamics in Continuous Media volume. In showing that the polarization vector is the dipole moment per unit volume of a dielectric, we get...
I feel silly but I've been looking at this equation for a while and I don't fully understand the individual steps taken to go from the top line to the bottom line:
I think I am getting caught up with all the r's in the equation. I recognize that on the second line "r" describes the point at...