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

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Presentation on theme: "ELECTROMAGNETICS AND APPLICATIONS Lecture 4 Poynting Vector in Complex Notation. EM Fields and Interfaces. Luca Daniel."— Presentation transcript:

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

2 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

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

4 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)

5 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

6 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!

7 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:

8 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 ss ss ss ss ss ss L3-8


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