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

2024
Views:

57

Pages:

6
Author:

Jabin F.

# Reflection & Transmission Coefficients R = (Power Reflected) / (Power Incident) = (Energy Reflected) / (Energy Incident) R = (Intensity Reflected) / (Intensity Incident) Power ∝ energy ∝ intensity ∝ (E₀)² Rn = (E₀r/E₀c)² = (n₁ - n₂) / (n₁ + n₂)² R₁ = (E₀r/E₀c)² = (n₁ - n₂) / (n₁ + n₂)² for normal incidence (θ₁ = 0°): Rn = R₁ = (n₁ - n₂) / (n₁ + n₂)² Tn = T₁ = 4n₁n₂ / (n₁ + n₂)² for energy conservation: R + T = 1 A plane electromagnetic wave of wavelength λ is incident on a circular loop of conducting wire. The loop radius is a (a << λ). The angle (in degree) made by the Poynting vector with the normal to the plane of the loop to generate a maximum induced electrical signal is 90°. Sol: maximum induced current or emf → emf = Ɛ = ∮_c E·dl = -∫_s ∂B/∂t·ds = -μ₀n₀(∂I/∂t) ∫_s ẑ·ds = -μ₀n₀(∂I/∂t) πa² Diagram: A circular loop with a radius a. A plane electromagnetic wave incident on the loop. The Poynting vector making an angle θ with the normal to the plane of the loop. Equation 3.2: Ei = E₀i exp[i(kz - ωt)] Er = E₀r exp[i(krz - ωt)] E₀t = E₀ti exp[i(ktz - ωt)] Vacuum to glass: n₁ = 1 n₂ = 1.5 (E₀r/E₀i) = (E₀r/E₀t) = (n₁ - n₂) / (n₁ + n₂) = (1 - 1.5) / (1 + 1.5) = -1/5 E₀t = 2 V/m E₀r = (-2/5) V/m (-) sign indicates change of phase by π (E₀t/E₀i) = (E₀t/E₀i) = (n₁ - n₂) / (n₁ + n₂) = 4/5 E₀t = (4/5) * 2 V/m E₀t = 8/5 V/m no phase change (option-c) R = (E₀r/E₀c)² → for E₀r and E₀c in the same medium. T = (E₀t/E₀c)² → because both E₀t and E₀i are in different media. Equation 3.3: E = E₀ exp[i(kz - ωt)]ĵ Medium 1: v₁, k₁, μ₁ Medium 2: v₂, k₂, μ₂ Given (v₂ > v₁), then m₁ > m₂. So denser to rarer → no phase change. Er = +E₀i exp[i(-kz - ωt)]ĵ Br = (kr x Er)/ω = (-ŷ) * (E₀/v₁) * exp[i(-kz - ωt)] Br = -ŷ (E₀/v₁) exp[i(-kz - ωt)]