Power Associated With EM Wave - Edubirdie

University:
Santa Fe College
Course:
ETS 2527C | Electromechanical Components and Mechanisms
Academic year:

2024
Views:

258

Pages:

5
Author:

Jabin F.

# Power associated with E.M. wave: (energy per unit time) Average power per cycle: P = ∫(S dot dA) Surface element: dA = dx dy dz Plane wave propagating in the z-direction: E = E₀ cos(kz - ωt) Magnetic field: H = (1/μ₀) * E₀ cos(kz - ωt) Poynting vector: S = (1/μ₀) * E x H = (1/2) * c * ε₀ * E₀² * k̂ Time-averaged power density: = (1/2) * c * ε₀ * E₀² Total power: P = * A = (1/2) * c * ε₀ * E₀² * a² Given: θᵢ = 30° n₁ = 1 n₂ = 2 Snell's Law: sin(θᵢ) / sin(θₜ) = n₂ / n₁ Calculation: sin(30°) / sin(θₜ) = 2 / 1 sin(θₜ) = 1/2 θₜ = 90° Conclusion: The angle of transmission (θₜ) is 90°. Equations: 𝐵 = (𝑅 × 𝐸) / 𝜔 𝐸 = -(𝑅 × 𝐵) / (μ₀ε₀) 𝐵 = μ₀𝐻 𝜔 = μ₀ε₀ 𝐸 = 𝐸₀εᵣ = 4ε₀ 𝐸 = [(î + αĵ + ĵ𝑘) / (4ω)] * 𝑅 * 𝐻₀ * cos(ωt - kz + φ) 𝐸 = (α² + 1) / (4ω) * (î + ĵ - 𝑘) * cos(ωt - kz + φ)

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