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An electromagnetic wave has Poynting vector S = (942 W/m²) cos²(10x - 3*10⁹ t) i-hat, with x in metres and t in seconds. Which statement is correct?

1. The electric field amplitude is about 600 N/C, i.e. E approx 600 cos(10x - 3*10⁹ t).
2. The magnetic field amplitude is about 2*10⁻⁶ T directed along i-hat.
3. The wave travels in the negative x direction.
4. The peak Poynting magnitude corresponds to E_rms approx 600 N/C.

Correct answer: The electric field amplitude is about 600 N/C, i.e. E approx 600 cos(10x - 3*10⁹ t).

Solution

The peak Poynting magnitude is S0 = c*epsilon0*E0² (since cos² has peak 1). Solving for E0 with S0 = 942 W/m² gives E0 approx 600 N/C. The phase (10x - omega t) indicates propagation in +x, so the +x options about direction (negative x) are wrong. The magnetic field is along the propagation-perpendicular direction, not i-hat, ruling out that option.

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