Chapter%2011

# Chapter%2011 - Dr. Ray Chen© Chapter 11 The Uniform Plane...

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Dr. Ray Chen© Chapter 11 The Uniform Plane Wave Dr. Ray Chen© 11.1 Wave motion in free space t E t E E t D J B , t B E ∂ ∂ = ∂ ∂ + = ∂ ∂ + = × ∇ ∂ ∂ − = × ∇ v v v v v v v v ε ε σ µ current without space in ( ) t B E E , t B E ∂ ∂ × −∇ = ∇ − ⋅ ∇ ∇ ∂ ∂ × −∇ = × ∇ × ∇ v v v v v 2 If = ⋅ ∇ = E , v v ρ 2 2 2 have we t E t E t t B E ∂ ∂ − = ∂ ∂ ∂ ∂ − = ∂ ∂ × −∇ = ∇ − v v v µε µε Dr. Ray Chen© 11.1 Wave motion in free space 2 2 2 t E E ∂ ∂ − = ∇ − v µε equation? difference partial order 2nd this of solution the s What' ( ) f. 2 frequency angular vector, wave : try s let' π ω ω γ = − ⋅ = : : k t k cos E E v v v v ( ) [ ] ( ) ( ) [ ] ( ) ( ) [ ] ( ) ( ) [ ] ( ) t k cos t k cos t t k sin t k cos t t k cos k t k cos t k sin k t k cos ω γ ω ω γ ω γ ω ω γ ω γ ω γ ω γ ω γ − ⋅ − = − ⋅ ∂ ∂ − ⋅ = − ⋅ ∂ ∂ − ⋅ − = − ⋅ ∇ − ⋅ ⋅ − = − ⋅ ∇ v v v v v v v v v v v v v v v v 2 2 2 2 , , Dr. Ray Chen© 11.1 Wave motion in free space ( ) ( ) : have thus we 2 2 = − ⋅ + − ⋅ − t k cos t k cos k ω γ µεω ω γ v v v v s / m c . k , k 8 2 2 2 2 10 3 1 : space free In × = = = = µε µε ω µεω wave. E.M. of velocity phase : k ω ( ) ( ) ( ) ( ) ( ) assume may we Since t k i e t k i e e E R t k cos E E , e B R t k cos B B t k cos E E ω γ ω γ ω γ ω γ ω γ − ⋅ − ⋅ = − ⋅ = = − ⋅ = − ⋅ = v v v v v v v v v v v v v v v Dr. Ray Chen© 11.1 Wave motion in free space ( ) ( ) ( ) t k i t k i e B i e E k i E ω γ ω γ ω − ⋅ − ⋅ ⋅ − − = × = × ∇ ∴ v v v v v v v v Ω = Ω = = = 120 377 space, free In ohm. of dimension a carries It medium. the of impedence intrinsic π ε µ ε ε µ µ ε µ , , : ε µ µ µε E k ˆ H H E k ˆ v v v × = ∴ = × E k ˆ k E k k...
View Full Document

## This note was uploaded on 08/15/2009 for the course EE 325 taught by Professor Brown during the Spring '08 term at University of Texas.

### Page1 / 25

Chapter%2011 - Dr. Ray Chen© Chapter 11 The Uniform Plane...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online