Oscillating dipole

In the near field, the equations are more complicated. For the oscillating dipole, you can still solve them, however. I'm guessing you focused on the far fields because they are simpler and give you a good idea of the distribution of polarization and power radiated.

 

I don't know how much you already know and what sort of explanation would help. But to describe it would take too long here, anyway. If you have a copy of Jackson's E&M text, look in chapters 8 and 9.

 

If the distance from the test point to one of the charges is r1 and the other charge is r2, when distance separating the dipole charges is significantly less than than r1 and r2, then the charges can be handled as if they were both an equal distance, r, from the test point (i.e. r=r1=r2). This simplifies the calculation. As you consider test points closer to the dipole, the difference in their distances, |r2-r1|, becomes a factor and you can no longer use the single distance r.

 

My apologies - you're looking at dipole radiation.

 

Yeah - at least that's so for analyzing the static dipole. For the dynamic case, (if you have JD Jacksons text on Classical Electrodynamics, see pg 411) he describes the difference between the "radation zone" (relatively far from the dipole) and the "near zone" where the E field predominates. The field in near zone behaves more like the static case.