〈 Berger | Dillon 〉

What do the colors and the different shades of colors mean when around that dot?

they're equipotential lines

The electric field in electrodynamics (in contradistinction with electrostatics) is not the gradient of a scalar potential. Also the potential itself is not a gauge invariant entity. So I think 'equipotential lines' don't have a physical significance. Am I missing something ? 1/2

well the scalar potential of a relativistically moving charge is indeed a well defined potential, this is how i colored the contour plot. However, they are only equipotentials if E = -grad(φ), which is generally not true in elec. dynamics https://en.wikipedia.org/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential …

so perhaps i was a bit sloppy with my terminology, however, they do correspond to lines of equal φ although that isn't technically a potential

Thanks for replying. But I humbly disagree. The Wikipedia calculation is in a certain choice of gauge i.e. Lorenz gauge. A different choice of gauge would yield a different $\phi$. E.g. $\phi=0$ in Coulomb gauge. In fact, $\phi$ can be chosen to be any function of spacetime ..1/n