Angular Momentum of the Electromagnetic Field
Overview1
The angular momentum stored in the electromagnetic field is as follows.
$$ \mathbf{\ell} = \mathbf{r} \times \mathbf{g}=\epsilon_{0}\big( \mathbf{r} \times (\mathbf{E} \times \mathbf{B} )\big) $$
$\mathbf{g}$ is the momentum density stored in the electromagnetic field.
Description
The electromagnetic field is not only a mediator of the electromagnetic forces acting between charges but also possesses energy itself.
$$ u =\dfrac{1}{2} \left( \epsilon_{0} E^2 + \dfrac{1}{\mu_{0}} B^2 \right) $$
It also possesses momentum, thus satisfying the law of conservation of momentum, which states that the sum of the momentum of matter and the momentum of the electromagnetic field is conserved.
$$ \mathbf{g} = \epsilon_{0} (\mathbf{E} \times \mathbf{B} ) $$
$$ \dfrac{d \mathbf{p}}{dt} =-\epsilon_{0}\mu_{0}\dfrac{d}{dt}\int_{\mathcal{V}} \mathbf{S} d\tau + \oint_{\mathcal{S}} \mathbf{T} \cdot d\mathbf{a} $$
And remarkably, the electromagnetic field also possesses angular momentum.
$$ \mathbf{\ell} = \mathbf{r} \times \mathbf{g}=\epsilon_{0}\big( \mathbf{r} \times (\mathbf{E} \times \mathbf{B} )\big) $$
Even static electromagnetic fields have angular momentum if $\mathbf{E} \times \mathbf{B} \ne 0$. The law of conservation of angular momentum applies to the total angular momentum, which is the sum of the angular momentum of matter and the angular momentum of the electromagnetic field.
David J. Griffiths, 기초전자기학(Introduction to Electrodynamics, 김진승 역) (4th Edition1 2014), p397 ↩︎