General formula for Electric field of a point charge

[elara]

While reading through the Feynman Lectures on Physics (volume 1, number 28) I have come across the formula for the electric field for a moving point charge - it's the equation labelled (1) on this page:

http://maxwellsociety.net/PhysicsCorner/InteractingParticles/AcceleratingCharges.html

Can anyone explain where this comes from?

The first term I recognise as Coulomb's law, but am right in thinking that the second accounts for the time it takes for the change in electric field to propagate to an observer? And then where does the last term come from? Do I need to just take this on faith until I get to volume 2?

Thanks for any help!

 

[Born2bwire]

In general, the fields from a charge are given by the Lienerd-Wiechert potentials. These are derived from Maxwell's equations though it isn't a particularly trivial derivation to do so. But in addition to the static coulomb field, there are the retarded fields due to the finite propagation of light and there is radiation that occurs due to any acceleration of charges. The latter would seem to be the cause of your third term in your referenced equation since it is related to the second order time derivative of the retarded position.

 

[Meir Achuz]

It's even more complicated than Eq. (1) looks. Taking tlme derivatives of retarded functions is a mess. You definitely have to wait until volume 2, or maybe a better book.