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An electromagnetic wave passing through the space is given by equations E=E₀ sin(ω t-kx), B=B₀ sin(ω t-kx). Which of the following is true ?

Asked in GSEB Board July 2017 · Reading omega, k, nu, lambda and v

• (1) E₀B₀=ω k
• (2) E₀ω=B₀k
• (3) E₀k=B₀ω
• (4) E₀k=B₀

Step-by-step solution

Why the other options are wrong

• (1) comes from multiplies the two amplitudes on one side and the two wave constants on the other. The two sides do not even have the same units, so it cannot hold.
• (2) comes from is the correct relation inverted: it gives (E₀)/(B₀)=k/ω=1/c, making E₀ much smaller than B₀ when in fact it is much larger.
• (4) comes from drops ω altogether, so the right-hand side is left with an extra factor of time: B₀ is V s m⁻² while E₀k is V m⁻². The equation is not even dimensionally consistent.

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