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

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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...
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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.

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

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