Editing Classical electromagnetism (section)

== General field equations ==
{{Main|Jefimenko's equations|Liénard–Wiechert potential}}

As simple and satisfying as Coulomb's equation may be, it is not entirely correct in the context of classical electromagnetism. Problems arise because changes in charge distributions require a non-zero amount of time to be "felt" elsewhere (required by special relativity).

For the fields of general charge distributions, the retarded potentials can be computed and differentiated accordingly to yield Jefimenko's equations.

Retarded potentials can also be derived for point charges, and the equations are known as the Liénard–Wiechert potentials. The [[scalar potential]] is:

:<math>
\varphi = \frac{1}{4 \pi \varepsilon_0} \frac{q}{\left| \mathbf{r} - \mathbf{r}_q(t_{\rm ret}) \right|-\frac{\mathbf{v}_q(t_{\rm ret})}{c} \cdot (\mathbf{r} - \mathbf{r}_q(t_{\rm ret}))}
</math>

where <math>q</math> is the point charge's charge and <math>\textbf{r}</math> is the position. <math>\textbf{r}_{q}</math>  and  <math>\textbf{v}_{q}</math>are the position and velocity of the charge, respectively, as a function of [[retarded time]]. The [[vector potential]] is similar:

:<math>
\mathbf{A} = \frac{\mu_0}{4 \pi} \frac{q\mathbf{v}_q(t_{\rm ret})}{\left| \mathbf{r} - \mathbf{r}_q(t_{\rm ret}) \right|-\frac{\mathbf{v}_q(t_{\rm ret})}{c} \cdot (\mathbf{r} - \mathbf{r}_q(t_{\rm ret}))}.
</math>

These can then be differentiated accordingly to obtain the complete field equations for a moving point particle.