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The rate at which electromagnetic energy is radiated is given by Lamor's formula. What is the corresponding rate at which momentum is radiated and hence force to this?

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The Abraham-Lorentz-Dirac radiation reaction four-force on an arbitrarily moving point charge of mass $m$ and charge $q$, due to radiated momentum, is, according to Dirac,

$$F_\mu^\text{rad}=\frac{\mu_0q^2}{6\pi mc}\left[\frac{d^2p_\mu}{d\tau^2}-\frac{p_\mu}{m^2c^2}\left(\frac{dp_\nu}{d\tau}\frac{dp^\nu}{d\tau}\right)\right],$$

where $p^\mu$ is the particle’s four-momentum and $\tau$ is the proper time along its worldline.

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  • $\begingroup$ Obvious now you've mentioned it. I was thinking of something using the retarded acceleration/momentum as with Lamor's formula. $\endgroup$ – Physiks lover May 17 at 22:22
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Larmor's formula isn't going to give you a force or momentum because it is a scalar equation telling you the total power radiated by an accelerated charge.

In order to know something about force/momentum you need to know the Poynting vector of the fields associated with the electromagnetic power, as a function of direction.

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  • $\begingroup$ I'm after a formula for the rate of momentum radiated by an accelerated charge derived like Lamor's power formula from the fields. $\endgroup$ – Physiks lover May 17 at 20:08

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