Changes

In cylindrical coordinates, <math>d^2r=rdrd\phi \quad</math>.  Without loss of generality, we consider a harmonic solution with a particular frequency &omega; = kc.

In cylindrical coordinates, <math>d^2r=rdrd\phi \quad</math>.  Without loss of generality, we consider a harmonic solution with a particular frequency &omega; = kc.

:<math>\dot{A}\left(\mathbf{r},t'-\frac{|\mathbf{r}-\mathbf{r}'|}{c}\right)=\dot{A}(\mathbf{r},0)e^{-ik(t'c-|\mathbf{r}-\mathbf{r}'|)}</math><br><br>

:<math>\dot{A}\left(\mathbf{r},t'-\frac{|\mathbf{r}-\mathbf{r}'|}{c}\right)=\dot{A}(\mathbf{r},0)e^{-ik(t'c-|\mathbf{r}-\mathbf{r}'|)}</math><br><br>

:<math>A(r')=\frac{z'\dot{A_0}}{2\pi c}\int_{z=0} rdrd\phi\, \frac{e^{-ik(t'c-|\mathbf{r}-\mathbf{r}'|)}}{|\mathbf{r}-\mathbf{r}'|^2}</math>

:<math>A(r')=\frac{z'\dot{A_0}}{2\pi c}\,e^{-i\omega t'} \int_{z=0} rdrd\phi\, \frac{e^{ik|\mathbf{r}-\mathbf{r}'|)}}{|\mathbf{r}-\mathbf{r}'|^2}</math>

== Special Case ==

== Special Case ==