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

For

T^{μν}

to be symmetric in every inertial frame, its mixed components must satisfy

T^{0 i} = c g_{i} = c ϵ_{0} (E \times B)_{i} = T^{i 0} = \frac{N _{i}}{c} = \frac{( E \times B ) _{i}}{μ _{0} c} .

For arbitrary fields this requires

μ_{0} ϵ_{0} = \frac{1}{c ^{2}} .

Solved by gpt-5.6-sol high.

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