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ELECTROMAGNETICS AND APPLICATIONS Lecture 4 Poynting Vector in Complex Notation. EM Fields and Interfaces. Luca Daniel

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L3-2 Review of Fundamental Electromagnetic Laws Electromagnetic Waves in Media and Interfaces oThe EM waves in homogenous Media oElectromagnetic Power and Energy The Poynting Theorem Wave Intensity Poynting Theorem in Complex Notation oEM Fields at Interfaces between Different Media Fields at boundaries: normal components Fields at boundaries: tangential components Fields inside perfect conductors Fields at boundaries of perfect conductors oEM Waves Incident “Normally” to a Different Medium oEM Waves Incident at General Angle to a Different Medium Today’s Outline Today

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L3-3 Power Flow in Uniform Plane Waves The time average is called “intensity” [W/m 2 ] of the wave 0 z

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L3-4 Poynting Vector in Complex Notation Defining a meaningful and relating it to is not obvious. It is easier to relate it to the intensity (time average): Thus the Intensity can put computed directly from the field phasors and Note: (by definition)

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L3-5 Review of Fundamental Electromagnetic Laws Electromagnetic Waves in Media and Interfaces oThe EM waves in homogenous Media oElectromagnetic Power and Energy The Poynting Theorem Wave Intensity Poynting Theorem in Complex Notation oEM Fields at Interfaces between Different Media Fields at boundaries: normal components Fields at boundaries: tangential components Fields inside perfect conductors Fields at boundaries of perfect conductors oEM Waves Incident “Normally” to a Different Medium oEM Waves Incident at General Angle to a Different Medium Today’s Outline

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Gauss’s Law: Therefore: surface charge density s surface S A h (assuming Lim h 0) Similarly L3-4 Fields at Boundaries: Normal Components i.e. normal B is always continuous!

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Faraday’s Law: Therefore: E 1// E 2// A h L Ampere’s Law: Alternatively: E 1// = E 2// (Lim h 0) Tangential E is always continuous Note that is only possible on perfect conductors L3-7 Fields at Boundaries: Tangential Components J s produces a jump in tangential H:

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Conducting Media Electric Fields in perfect conductors : Constitutive relation for conducting medium (Ohm’s Law): where σ is the conductivity [Am/V] which would instantaneously generate surface charge that immediately canceling all E. In a regular conductor charges are free to move. If E is applied, J will generate charges on the surface that start cancelling the applied E (charge relaxation). Therefore inside perfect conductors: = 0 E out // = E in // = 0 => E fields can only be to a perfect metal surface can only be on the surface since any charge inside would produce E and J that would instantaneously distributed it to the surface q J J J J J J ss ss ss ss ss ss L3-8

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