Lect16Isotropic

# Lect16Isotropic - 1 ECE 3030 Electromagnetic Fields and...

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Unformatted text preview: 1 ECE 3030 Electromagnetic Fields and Waves Fall 2009 Lecture 16 2009/10/2 Waves in Isotropic Media Dielectrics and Conductors 1 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 16: Instructor: Dr. Wesley E. Swartz σ ε δ z e − z E lec16_1.avi Review: Plane Waves in Free Space • Faraday’s Law: • Ampere’s Law: • Complex Wave Equation: – Assume ( ) ( ) r H j r E o μ ω − = × ∇ ( ) ( ) ( ) r E j r J r H o ε ω + = × ∇ ( ) ( ) = = r r J ρ ( ) ( ) ( ) r E r H j r E o o 2 o ε μ ω μ ω = × ∇ − = × ∇ × ∇ 3 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 16: • The E- and H-field phasors for a plane wave in free space are: ( ) ( ) ( ) ( ) ( ) ( ) r E r E r E r E r E o o 2 2 o o 2 2 ε μ ω ε μ ω − = ∇ = ∇ − • ∇ ∇ ( ) r k j o e E n ˆ r E • − = ( ) ( ) r k j o o e E n ˆ k ˆ r H • − × = η E H k Ω ≈ = 377 o o o ε μ η c k o o ω ε μ ω = = Wave Equations in Dielectric Media • Suppose we have a plane wave of the form, – traveling in an infinite dielectric medium with permittivity ε • What is different from wave propagation in free space? – Faraday’s Law: ( ) r k j o e E n ˆ r E • − = E H ε ( ) ( ) r H j r E o μ ω − = × ∇ 4 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 16: – Ampere’s Law: – Complex Wave Equation: • Assume: ( ) ( ) ( ) r E j r J r H ε ω + = × ∇ ( ) ( ) = = r r J ρ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) r E r E r E r E r E r E r H j r E o 2 2 o 2 2 o 2 o ε μ ω ε μ ω ε μ ω μ ω − = ∇ = ∇ − • ∇ ∇ = × ∇ − = × ∇ × ∇ Compare with the complex wave equation in free space ( ) ( ) r E r E o o ε μ ω 2 2 − = ∇ Dispersion Relations of Dielectric Media • Substitute the plane wave solution into the complex wave equation to get ( ) r k j o e E n r E . ˆ − = E H ε ( ) ( ) r E r E o ε μ ω 2 2 − = ∇ ( ) ( ) ε μ ω ε μ ω o r E r E k k r E r E 2 2 2 − = ∇ 5 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 16: ( ) ( ) ε μ ω ε μ ω o o k r E r E k k 2 2 . = − = − Compare with for waves in free space ε μ ω o k = Define the refractive index “ n ” of a dielectric medium as: o n ε ε = o o k ε μ ω = Waves in Dielectric Media – Velocity • A plane wave • Has a dispersion relation given by ( ) r k j o e E n ˆ r E • − = E H ε...
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Lect16Isotropic - 1 ECE 3030 Electromagnetic Fields and...

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