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A floodlight covered with a red filter emits a sinusoidal plane wave whose electric field is given by Ex = 36 sin(1.20 * 10⁷ * z - 3.6 * 10¹⁵ * t) V/m. The average intensity of the beam is approximately sqrt(n) W/m², where n is a positive integer. Find n.

1. 1
2. 2
3. 3
4. 4

Correct answer: 1

Solution

Average intensity of an electromagnetic wave: I = E0² / (2 * mu0 * c) where mu0 = 4*pi*10⁻⁷ T*m/A, c = 3*10⁸ m/s. mu0 * c = 4*pi*10⁻⁷ * 3*10⁸ = 4*pi*30 = 120*pi ≈ 376.99 ohms I = (36)² / (2 * 376.99) = 1296 / 753.98 ≈ 1.718 W/m² I ≈ sqrt(n) => sqrt(n) ≈ 1.718 => n ≈ 2.95 ≈ 3. So n = 3.

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