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Maxwell stress tensor

With electromagnetic momentum density

g = ϵ_{0} E \times B

, the momentum-flux convention

σ_{ij} = - ϵ_{0} E_{i} E_{j} + \frac{ϵ _{0}}{2} E^{2} δ_{ij} - \frac{1}{μ _{0}} B_{i} B_{j} + \frac{1}{2 μ _{0}} B^{2} δ_{ij}

satisfies

\partial_{t} g_{j} + \partial_{i} σ_{ij} = - (ρ E + J \times B)_{j} .

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