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Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 4 / 5D / c / Solution

The Poynting vector is

S = \frac{1}{μ _{0}} E \times B = \frac{ω}{μ _{0} k} (B_{1}^{2} + B_{2}^{2}) cos^{2} (k z - ω t) e_{z} .

It is the electromagnetic energy flux in the propagation direction; its time average is

c (B_{1}^{2} + B_{2}^{2}) / (2 μ_{0})

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Solved by gpt-5.6-sol high.

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