EM_waves - Electromagnetic Waves Maxwell's Eqs....

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EM waves Electromagnetic Waves and Optics 1 Electromagnetic Waves •M a x w e l l s E q s . • Electromagnetic waves in vacuum • Energy and momentum transport • EM wave interactions with matter EM waves Electromagnetic Waves and Optics 2 Maxwell’s Equations differential form: » Lorentz force: t E J B t B E B E + = × = × = = r r r r r r r r r r r 0 0 0 0 0 µ ε ρ B v q E q F r r r r × + = integral form: ∫∫ ∫∫ ∫∫ ∫∫ + = = = = Σ Σ S d E t l d B S d B t l d E S d B q S d E in in i r r r r r r r r r r r r 0 0 0 0 0 1
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EM waves Electromagnetic Waves and Optics 3 Gauss’s Law flux of E-field: – closed surface E-field lines – start on positive – end on negative point charge Î Coulomb’s Law “longitudinal” field 0 ε ρ = E r r in q S d E Σ = ∫∫ 0 1 r r + 2 0 0 1 4 r q E q dS E πε = = ∫∫ 0 2 = ∫∫ S d E r r ∫∫ = Φ S d E E r r S d r E r EM waves Electromagnetic Waves and Optics 4 Faraday’s Law flux of B-field: – open surface E-field lines – induction changing B – circulate; no beginning or end example: solenoid with AC current – B change opposed by induced emf “transverse” field —no longer “attached” to charges t B E = × r r ∫∫ = S d B t l d E r r r r ∫∫ = Φ S d B B r r B t l d E Φ = r r
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This note was uploaded on 08/26/2008 for the course PHYSICS 603 taught by Professor Sage during the Summer '06 term at Northwestern.

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EM_waves - Electromagnetic Waves Maxwell's Eqs....

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