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?
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$\begingroup$ Related: physics.stackexchange.com/q/7218/2451 and physics.stackexchange.com/q/23585/2451 $\endgroup$– Qmechanic ♦Jan 21, 2013 at 9:57
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Well, Newton's third law is just conservation of momentum...
$$F_1 = -F_2 \Rightarrow \frac{dp_1}{dt} + \frac{dp_2}{dt} = 0$$
answered Oct 25, 2011 at 22:51
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1$\begingroup$ The point is that Newton's third law fails for point charges in motion with a magnetic interaction. $\endgroup$ Oct 25, 2011 at 23:21
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$\begingroup$ But conservation of momentum doesn't in general (I can't think about an example of failure now) isn't it? $\endgroup$ Oct 25, 2011 at 23:32
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2$\begingroup$ Conservation of momentum works, Newton's third law fails, because there is field momentum. This can lead to paradoxical forces even when the field is not radiating. $\endgroup$ Oct 25, 2011 at 23:38