An electromagnetic wave in free space has E⃗ = 10 cos(10⁷t + kx) ĵ V/m. Determine which statements about its wavelength, wave number, amplitude and direction are correct.
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Question

An electromagnetic wave in free space has E⃗ = 10 cos(10⁷t + kx) ĵ V/m. Determine which statements about its wavelength, wave number, amplitude and direction are correct.

G1 Physics · Accepted Answer

Step 1: Compare E⃗ = 10 cos(10⁷t + kx) ĵ V/m with a plane wave. Step 2: Amplitude E₀ = 10 V/m; angular frequency ω = 10⁷ rad/s. Step 3: k = ω/c = (10⁷)/(3 × 10⁸) = 1/30 ≈ 0.0333 rad/m. Step 4: λ = 2π/k = 60π ≈ 188.5 m. Step 5: The plus sign in (ωt + kx) means propagation in the negative x-direction. Thus (I) and (III) are true, while (II) and (IV) are false. Final answer: (D) (I) and (III).