Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 1 / 37B / d

Let $J_k=\int {ϵ}_{k\ell j}{x}_{\ell }{g}_j{d}^{3}x$. Local momentum conservation and integration by parts, with the boundary term vanishing for a localized field, givebecause ${\sigma }_{ij}$ is symmetric. Hence the total electromagnetic angular momentum is independent of time.