The electric field of an electromagnetic wave in vacuum is directed along +y and has magnitude E = 150 cos(2x - 6×10⁸t) V/m. The corresponding magnetic field is:
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Question

The electric field of an electromagnetic wave in vacuum is directed along +y and has magnitude E = 150 cos(2x − 6×10⁸t) V/m. The corresponding magnetic field is:

G1 Physics · Accepted Answer

The phase 2x − 6×10⁸t shows propagation along +x. Wave speed: v = ω/k = (6×10⁸)/2 = 3×10⁸ m/s. Thus the wave is travelling in vacuum. Magnetic-field amplitude: B₀ = E₀/c = 150/(3×10⁸) = 5×10⁻⁷ T. E is along +y and propagation is along +x. Therefore B must be along +z because (+y) × (+z) = +x. Hence the magnetic field is along +z with magnitude 5×10⁻⁷ cos(2x − 6×10⁸t) T. Correct option: A.