# Electrical work and Coulomb's law

In some text books I've encountered the calculation of electrical work done on a point charge moving in an electric field (e.g. when demonstrating that electric force is conservative) is done by making use of Coulomb's law. However, Coulomb's law is not valid in case of moving charges, and therefore, cannot be used for this purpose. There's clearly something I am missing, but can't figure out what.

• Neglecting Bremsstrahlung Coulomb's law is valid for moving charges as long as the electric field they are moving in is constant. For classical slowly moving charges this is an excellent approximation. Commented Jan 30, 2016 at 20:56
• Also in these derivations one can think of "infinitely slow" movement, allowing arbitrarily close approximation.
– Danu
Commented Jan 30, 2016 at 21:11
• So it's just a low velocity approximation. I wish it were mention in those books... Thanks Commented Jan 30, 2016 at 21:23
• No it is not an approximation: PE is defined as the work in infinitesimally slow motion. Commented Jan 8, 2021 at 22:07
• Does this answer your question? How can moving electrons participate in electrostatic interaction? Commented Jan 8, 2021 at 22:24