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# 161_1_Class2 - EE161 Electromagnetic Waves Spring 2010 Prof...

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Unformatted text preview: EE161 Electromagnetic Waves Spring, 2010 Prof. Y. Ethan Wang Electrical Engineering Dept. UCLA Lesson 2 • Boundary Conditions in PEC • Complex Variable & Phasor • Time-harmonic Maxwell’s equations • Wave Equations Summary of Boundary Conditions ) ( ) ( ) ( ) ( 2 1 2 1 2 1 2 1 = − ⋅ = − ⋅ = − × = − × B B i D D i J H H i E E i n S n S n n ρ n i Unit normal to the surface 1 2 boundary In scalar forms 2 1 2 1 2 1 2 1 = − = − = − = − n n S n n S t t t t B B ρ D D J H H E E In vector forms Application of boundary conditions are essential in solving Maxwell equations in differential form Boundary Conditions on Dielectrics n i Unit normal to the surface 1 2 boundary 2 1 2 1 2 1 2 1 = − = − = − = − n n S n n S t t t t B B ρ D D J H H E E 1 σ 2 σ , 2 1 = ⇒ s J finite σ σ 2 1 t t E E = 2 1 t t H H = The conclusion is: Boundary Conditions on PEC n i Unit normal to the surface 1 2 boundary 2 1 2 1 2 1 2 1 = − = − = − = − n n S n n S t t t t B B ρ D D J H H E E 1 σ 2 σ ∞ → 2 σ S n J H i = × 1 ∞ → 2 σ 2 1 = = t t E E ∞ → 2 σ 2 1 = = n n B B ∞ → 2 σ S n D ρ = 1 2 2 2 2 = = = = D B H E (inside PEC) Maxwell’s Equations and Boundary Conditions in One Glance Integral Form Differential Form Boundary Conditions ∫ ∫ ⋅ − = ⋅ S C dS dt d dl B E ∫ ∫ ∫ ⋅ + ⋅ = ⋅ S S C dS dt d dS dl D J H ∫ ∫ = ⋅ V S dv dS ρ D ∫ = ⋅ S dS B t ∂ ∂ −...
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161_1_Class2 - EE161 Electromagnetic Waves Spring 2010 Prof...

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