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An electromagnetic wave travels along the x-axis with a wavelength of 8 mm. Its electric field oscillates along the y-axis and has a peak value of 60 V/m. If the wave moves through vacuum, identify the correct expressions for the electric and magnetic fields.

1. E_y = 60 sin[(pi/4)*10³ (x - 3*10⁸ t)] j^ V/m, B_z = 2 sin[(pi/4)*10³ (x - 3*10⁸ t)] k^ T
2. E_y = 60 sin[(pi/4)*10³ (x - 3*10⁸ t)] j^ V/m, B_z = 2*10⁻⁷ sin[(pi/4)*10³ (x - 3*10⁸ t)] k^ T
3. E_y = 2*10⁻⁷ sin[(pi/4)*10³ (x - 3*10⁸ t)] j^ V/m, B_z = 60 sin[(pi/4)*10³ (x - 3*10⁸ t)] k^ T
4. E_y = 2*10⁻⁷ sin[(pi/4)*10⁴ (x - 4*10⁸ t)] j^ V/m, B_z = 60 sin[(pi/4)*10⁴ (x - 4*10⁸ t)] k^ T

Correct answer: E_y = 60 sin[(pi/4)*10³ (x - 3*10⁸ t)] j^ V/m, B_z = 2*10⁻⁷ sin[(pi/4)*10³ (x - 3*10⁸ t)] k^ T

Solution

For an EM wave in vacuum, the magnetic field amplitude is much smaller than the electric field amplitude, related by B0 = E0/c. The electric field keeps its given amplitude 60 V/m, so options listing E0 = 2*10⁻⁷ are wrong. The wave number must match lambda = 8 mm, giving k = (pi/4)*10³, and the speed factor must be c = 3*10⁸ m/s.

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