Length Contraction | Lecture Note - Edubirdie

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

2024
Views:

139

Pages:

6
Author:

Jabin F.

Dimension || to velocity is contracted. x' = x0 y' = y0 = √(1 - v^2/c^2) * y0 γ = 1/√(1 - v^2/c^2) = 1/√(1 - β^2) β = v/c σ' = 2Y / (y0 + Y0) = Yσ / (Y0 + σ) Emoving = σ' / ε0 = (Yσ / ε0) * (1/2) = Y * Eres / ε0 ⃗v = v0ŷ, ⃗E = E0ẑ ⇒ ⃗E ⊥ ⃗v Emoving = Y * Eres Section 1 Reference: Question 67, Page-91 Equations: k = (1/c) * √(ω^2 - ωc^2) ωc = cπ * √(1/l^2 + 1/l^2) = √(2) * cπ / L Section 2 Derivation: c^2k^2 = ω^2 - ωc^2 2kdk * c^2 = 2ωdω dω/dk = vg = ωc^2 / k ω^2 = c^2k^2 + ωc^2 ω = √(c^2k^2 + ωc^2) vg = (kc^2) / √(c^2k^2 + 2c^2π^2/l^2) = Lkc / √(L^2k^2 + 2π^2) Section 1 Reference: Question 68, Page-92 Given: a = 2m, b = 1m ω = 10^9 rad/sec Equation: (ωc)mn = cπ * √((m/a)^2 + (n/b)^2) Conclusion: TE10 is the dominant mode. Section 2 Calculation: (ωc)20 = 2cπ / a (ωc)20 = 3x10^8 * 3.14 (ωc)20 = 942.48x10^8 rad/sec Comparison: ω = 10x10^8 < (ωc)20 Conclusion: TE20 is supported. Calculation: (ωc)11 = cπ * √((1/a)^2 + (1/b)^2) (ωc)11 = √5 * cπ / 2 (ωc)11 > 10^9 rad/sec Conclusion: TE11 is not possible.

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