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The electric field in a plane electromagnetic wave is given by E_z = 60 cos(5x + 1.5×10⁹ t) V/m. Then expression for the corresponding magnetic field is (here subscripts denote the direction of the field):
B₀ = 60 / (3 × 10⁸) = 2 × 10⁻⁷ T, and E_z (k̂) ⟹ B must be along ŷ (ĵ) because k̂ × ĵ = -î!
In a vacuum / free space, the ratio of electric field amplitude to magnetic field amplitude equals the speed of light c = ω / k:
The direction of electromagnetic wave propagation is given by the unit vector along the Poynting vector Ŝ = Ê × B̂. Here, the wave travels in the negative x-direction (-î) and E is polarized along the z-axis (k̂):
The magnetic field oscillates in phase with the electric field in a plane EM wave:
Diagnose every choice: Know exactly why the right option works and why distractors fail.
100% correct. B₀ = 2 × 10⁻⁷ T, orientation along y-axis satisfies Ê × B̂ = -î, and phase matches E_z.
Incorrect. EM waves are transverse; B cannot oscillate along the direction of propagation (x-axis).
Incorrect. E and B cannot oscillate along the same axis (z), and amplitude is not divided by c.
Incorrect. Amplitude not scaled by c and phase arbitrarily changed from cosine to sine.
Students often pick B_x without thinking. In an EM wave traveling along x, NEITHER E nor B can have an x-component (transverse nature: E ⟂ B ⟂ v).
"E and B are mutually perpendicular, perpendicular to propagation, in phase, and related by E₀ = c B₀."
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