See attached scanned pages of page 118(left side) and page 125(right side) of Antenna Theory by Balanis.
On the left side, it is just some basic EM where
\[\nabla\times \vec {E}=-\frac{\partial {\vec {B}}}{\partial {t}}\;\Rightarrow\;\vec {E}=-\nabla {V}-\frac{\partial {\vec {A}}}{\partial {t}}\]
Then to Lorentz thingy \[\nabla\cdot \vec {A}=-\mu\epsilon \frac{\partial {V}}{\partial {t}}\].
And so on......
The only thing different is it is in time harmonic form where \[\frac{\partial{}}{\partial {t}}\rightarrow\;j\omega\].
Now going to the right side. I underlined the sentence that I have no idea where that comes from!! What is \[\frac {1}{r^n}=0\] where n=,2,3,4.....
Please explain what is that. This supposed to be very basic thing that
\[\vec {B}=\nabla\times\vec {A}\]
Then for far field where it is assumed plane wave,\[\vec {E}=\eta\hat {R} \times \vec {H}\]
Please help.
Thanks