An electromagnetic plane wave has a z-directed electric field of magnitude E = 60 cos(5x + 1.5 × 10⁹t) V/m. Which expression describes its magnetic field? The parenthesized labels specify field directions.
Options

Question

An electromagnetic plane wave has a z-directed electric field of magnitude E = 60 cos(5x + 1.5 × 10⁹t) V/m. Which expression describes its magnetic field? The parenthesized labels specify field directions.

Options

G1 Physics · Accepted Answer

Step 1: Compare the phase with cos(kx + ωt): k = 5 rad/m, ω = 1.5 × 10⁹ rad/s. The wave travels in the −x direction. Step 2: Speed = ω/k = (1.5 × 10⁹)/5 = 3 × 10⁸ m/s. Step 3: For an EM wave E₀/B₀ = c, so B₀ = 60/(3 × 10⁸) = 2 × 10⁻⁷ T. Step 4: The electric field points in z; for E × B to point −x, the magnetic field must point +y. Step 5: E and B are in phase. Final answer: B (y-component) = 2 × 10⁻⁷ cos(5x + 1.5 × 10⁹t) T, Option A.