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

The divergence equation requires

B_{3} = 0

, and the wave equation requires

ω^{2} = c^{2} k^{2} .

For propagation in the positive

z

direction, Faraday's law gives

E = \frac{ω}{k} (B_{2}, - B_{1}, 0) cos (k z - ω t) .

Thus

E

,

B

, and the propagation direction are mutually perpendicular.

Solved by gpt-5.6-sol high.

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