Introduction to Electrodynamics · Problem 11.27

Radiation carries away not just energy, but also momentum and angular momentum—quantities that scale with the fields far from the charge. The key is to use the momentum and angular momentum density in the electromagnetic field ($\mathbf{g} = \epsilon_0(\mathbf{E} \times \mathbf{B})$ and $\boldsymbol{\ell} = \mathbf{r} \times \mathbf{g}$) and integrate over a sphere at infinity, just as you did for energy flux with the Poynting vector. The radiation fields from an accelerating charge carry a definite directional and rotational character that depends on $\mathbf{a}$ and $\mathbf{v}$.

Radiation carries away not just energy, but also momentum and angular momentum—quantities that scale with the fields far from the charge. The key is to use the momentum and angular momentum density in the electromagnetic field ($\mathbf{g} = \epsilon_0(\mathbf{E} \times \mathbf{B})$ and $\boldsymbol{\ell} = \mathbf{r} \times \mathbf{g}$) and integrate over a sphere at infinity, just as you did for energy flux with the Poynting vector. The radiation fields from an accelerating charge carry a definite directional and rotational character that depends on $\mathbf{a}$ and $\mathbf{v}$.