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

Asked in GSEB Board March 2016 · Reading omega, k, nu, lambda and v

• (1) E₀ω = B₀ k
• (2) E₀ B₀ = ω k
• (3) E₀ k = B₀ω
• (4) (E₀)/(B₀) = 1/(ω k)

Step-by-step solution

Why the other options are wrong

• (1) This is the relation upside down: it gives (E₀)/(B₀) = k/ω = 1/c, which would make the electric amplitude smaller than the magnetic one by a factor c instead of larger.
• (2) The product of the two amplitudes is not fixed by the wave -- only their ratio is. The units do not match either: E₀B₀ against ω k, which is s⁻¹ m⁻¹.
• (4) (E₀)/(B₀) must equal c, the same constant for every wave in vacuum, whereas 1/(ω k) changes from one wave to the next; the units are wrong as well.

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