# What is the force corresponding to Lamor's formula for EM radiated power?

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?

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.

• Obvious now you've mentioned it. I was thinking of something using the retarded acceleration/momentum as with Lamor's formula. – Physiks lover May 17 at 22:22

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.

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