c2 - Forces F x = dU dx V dQ dx U = IZZ ε ~ E ~ E 2 dV U...

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Unformatted text preview: Forces F x =- dU dx + V dQ dx U = IZZ ε ~ E · ~ E 2 dV U cap = 1 2 CV 2 Electromagnetic Power-Energy Continuity Equation ~ S ( ~ r,t ) = ~ E ( ~ r,t ) × ~ H ( ~ r,t ) W ( ~ r,t ) = μ ~ H ( ~ r,t ) · ~ H ( ~ r,t ) 2 | {z } m-field en. density + ε ~ E ( ~ r,t ) · ~ E ( ~ r,t ) 2 | {z } e-field en. density -∇ ~ S ( ~ r,t ) = ∂W ( ~ r,t ) ∂t + ~ J ( ~ r,t ) · ~ E ( ~ r,t )- IZ ~ S ( ~ r,t ) = ∂ ∂t IZZ W ( ~ r,t ) dV + IZZ ~ J ( ~ r,t ) · ~ E ( ~ r,t ) dV { net power flow } = rate of increase of total energy in closed volume + rate of total energy loss thru diss. Electromagnetic Waves f = λv,c = 1 / √ ε μ ∼ 3 × 10 8 m/s,η = p μ /ε ∼ 377Ω Time Harmonic Fields ~ E ( ~ r,t ) = ˆ nE cos( ωt- ~ k · ~ r ) ~ H ( ~ r,t ) = ( ~ k × ˆ n ) E η cos( ωt- ~ k · ~ r ) ~ k · ˆ n = 0 , k 2 = ~ k · ~ k,ω = kc ~ E ( ~ r,t ) = < n ~ E ( ~ r ) e jωt o , ~ E ( ~ r ) = ˆ nE e- j ~ k · ~ r Maxwell’s Equations (Complex Phasor Notation) (Gauss, Gauss, Faraday, Ampere) ∇ · ε ~ E ( ~ r ) = ρ ( ~ r ) (1) ∇ · μ ~ H ( ~ r ) = (2) ∇ × ~ E =- jωμ ~ H ( ~ r ) (3) ∇ × ~ H = ~ J ( ~ r ) + jωε ~ E ( ~ r ) (4) Complex Poynting Vector ~ E ( ~ r ) = ˆ nE e- j ~ k · ~ r ~ H ( ~ r ) = ˆ k × ˆ n E η e- j ~ k · ~ r ~ S ( ~ r ) = ~ E ( ~ r ) × ~ H * ( ~ r ) D ~ S ( ~ r ) E = 1 2 < n ~ S ( ~ r ) o = 1 2 < ˆ n × ˆ k × ˆ n * E 2 η Wave Propagation in Dielectric Medium n = p ε/ε k = ω √ μ ε = ω n c = 2 π λ λ = 2 πc ωn η = r μ ε Wave Propagation in Conductive Medium ε eff ( ω ) = ε 1- j σ ωε n eff ( ω ) = s ε eff ( ω ) ε = r ε ε r 1- j σ ωε k = ω √ μ ε s ε eff ( ω ) ε = ω n eff ( ω ) c k = k- jk 00 η eff ( ω ) = r μ ε eff ( ω ) 1 η eff ( ω ) = k ωμ = k- jk 00 ωμ D ~ S (...
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This note was uploaded on 04/15/2008 for the course ECE 3030 taught by Professor Rana during the Fall '06 term at Cornell.

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c2 - Forces F x = dU dx V dQ dx U = IZZ ε ~ E ~ E 2 dV U...

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