Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 36D / b / Solution

The tensor ${\sigma }_{ij}$ is the flux of the $j$th component of electromagnetic momentum across a surface normal to the $i$ direction, with the sign convention used in the conservation law. Its diagonal components are normal momentum fluxes, interpreted as electromagnetic pressures or tensions. Its off-diagonal components are tangential momentum fluxes, interpreted as shear stresses.