The electric field of an electromagnetic wave is Eₓ = 0, Eᵧ = 2.5 cos[(2π × 10⁶ rad/s)t - (π × 10⁻² rad/m)x] N/C, E(z) = 0. Find its direction, frequency and wavelength.
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Question

The electric field of an electromagnetic wave is Eₓ = 0, Eᵧ = 2.5 cos[(2π × 10⁶ rad/s)t − (π × 10⁻² rad/m)x] N/C, E(z) = 0. Find its direction, frequency and wavelength.

G1 Physics · Accepted Answer

Step 1: Standard travelling-wave form is E = E₀cos(ωt − kx). Step 2: Compare ω = 2π × 10⁶ rad/s and k = π × 10⁻² rad/m. Step 3: Frequency f = ω/(2π) = 10⁶ Hz. Step 4: Wavelength λ = 2π/k = 2π/(π × 10⁻²) = 200 m. Step 5: The phase (ωt − kx) describes propagation along positive x. Final answer: (C) +x direction, 10⁶ Hz, 200 m.