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By which one of the following equations are the magnitudes of the electric and magnetic fields in an electromagnetic wave related?

Asked in GSEB Board July 2022 · E0 = cB0 and E/B = c

• (1) E₀ = (B₀)/C
• (2) B₀ = (E₀)/C
• (3) E₀ = (B₀²)/(2C)
• (4) B₀ = (E₀²)/(2C)

Step-by-step solution

Why the other options are wrong

• (1) This is the ratio upside down. It makes the electric amplitude the smaller of the two by a factor C: for B₀ = 1 T it would give E₀ = 3.3×10⁻⁹ V m⁻¹ instead of 3×10⁸ V m⁻¹.
• (3) The square and the factor 2 are borrowed from the energy density u = 1/2ε₀E². The link between the amplitudes themselves is linear: double B₀ and E₀ doubles.
• (4) The same borrowed square and factor 2, with the fields the right way round. A squared field cannot equal a field -- the two sides do not even carry the same units.

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