soft question - Is classical electromagnetism a dead research field?

1. Is classical electromagnetism a dead research field?


2. Are there any phenomena within classical electromagnetism that we have no explanation for?

Answer

J. D. Jackson in the introductory remarks of his chapter on 'Radiation Damping, Classical Models of Charged Particles' (3rd edition), says that the problem of radiation reaction on motion of charged particles is not yet solved. He says that we know how to find motion of charged particles in given configuration of EM fields and also how to calculate EM fields due to given charge and current densities. However, when a charged particle accelerates in a field, it also radiates and we usually ignore the radiation reaction.

You can also refer to the paper

The basic open question of classical electrodynamics. Marijan Ribarič and Luka Šušteršič. arXiv:1005.3943.

If you consider plasma physics and magnetohydrodynamics to be part of classical electrodynamics your list of open problems may grow.