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

2024
Views:

193

Pages:

6
Author:

Jabin F.

EM Radiation:- It is Coupled oscillations of E & B propagating with speed of light in vacuum. ⇒ ∇²E = ε₀μ₀ \frac{∂²E}{∂t²} -(i) ∇×E = -\frac{∂B}{∂t} -(ii) ∇⋅B = 0 -(iii) ∇×B = μ₀J + μ₀ε₀ \frac{∂E}{∂t} -(iv) #let k² = ω²/c² (propagating along +z dirn) E = Ek (wave is polarized along x-dirn) k² = k²E^x + k²E^y Amplitude of wave is fixg Plane (Em wave propagation) k² = (k²)² (k²)² = (ω²/c²)² E = E₀e^(ikz - iωt) B = B₀e^(ikz - iωt) These equation of plane EM wave travelling along +z dirn. E₀ = amplitude of E field B₀ = amplitude of B field ⇒ kz - ωt = 0 z = \frac{ωt}{k} Wave representation, E = E₀ sin(kz - ωt) + φ E = E₀ sin(kz - ωt) + φ φ = π ⇒ kz + ωt = 0 z = -\frac{ωt}{k} Ex-(ii) E = E₀ sin(\frac{ky}{2} - \frac{\sqrt{3}kz}{2} + ωt) -(i) KE? → Standard wave equation - E = E₀ sin(ky - ωt) or E = E₀ sin(ky + ωt) Compare (i) and (ii) R = -[\frac{k}{2}\hat{y} - \frac{\sqrt{3}}{2}k\hat{z}] K = -\frac{k}{2}\hat{y} + \frac{\sqrt{3}}{2}k\hat{z} tanθ₂ = \frac{k/2}{\sqrt{3}k/2} = \frac{1}{\sqrt{3}} θ₂ = 60° mathematical B = \frac{R × E}{ω} = \frac{(-k/2\hat{y} + \sqrt{3}k/2\hat{z}) × E\hat{x}}{ω} KE = \frac{kE}{2}(\hat{z} + \hat{y}) tanθ₂ = \frac{\sqrt{3}/2}{\frac{1}{2}} = \sqrt{3} θ₂ = 60°