Is there a Newton's third law for the em field?

Question

There is a momentum associated with the em field that ensures the conservation of total momentum for a system of interacting charges.

Can the same be done in an analagous way to ensure Newton's third law is also true?

Answer 1

Well, Newton's third law is just conservation of momentum...

$$F_1 = -F_2 \Rightarrow \frac{dp_1}{dt} + \frac{dp_2}{dt} = 0$$