Lect16Isotropic - 1 ECE 3030 Electromagnetic Fields and...

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Unformatted text preview: 1 ECE 3030 Electromagnetic Fields and Waves Fall 2009 Lecture 16 2009/10/2 Waves in Isotropic Media Dielectrics and Conductors 1 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves Fall 2009 Lecture 16: Instructor: Dr. Wesley E. Swartz z e z E lec16_1.avi Review: Plane Waves in Free Space Faradays Law: Amperes Law: Complex Wave Equation: Assume ( ) ( ) r H j r E o = ( ) ( ) ( ) r E j r J r H o + = ( ) ( ) = = r r J ( ) ( ) ( ) r E r H j r E o o 2 o = = 3 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves Fall 2009 Lecture 16: The E- and H-field phasors for a plane wave in free space are: ( ) ( ) ( ) ( ) ( ) ( ) r E r E r E r E r E o o 2 2 o o 2 2 = = ( ) r k j o e E n r E = ( ) ( ) r k j o o e E n k r H = E H k = 377 o o o c k o o = = Wave Equations in Dielectric Media Suppose we have a plane wave of the form, traveling in an infinite dielectric medium with permittivity What is different from wave propagation in free space? Faradays Law: ( ) r k j o e E n r E = E H ( ) ( ) r H j r E o = 4 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves Fall 2009 Lecture 16: Amperes Law: Complex Wave Equation: Assume: ( ) ( ) ( ) r E j r J r H + = ( ) ( ) = = r r J ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) r E r E r E r E r E r E r H j r E o 2 2 o 2 2 o 2 o = = = = Compare with the complex wave equation in free space ( ) ( ) r E r E o o 2 2 = Dispersion Relations of Dielectric Media Substitute the plane wave solution into the complex wave equation to get ( ) r k j o e E n r E . = E H ( ) ( ) r E r E o 2 2 = ( ) ( ) o r E r E k k r E r E 2 2 2 = 5 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves Fall 2009 Lecture 16: ( ) ( ) o o k r E r E k k 2 2 . = = Compare with for waves in free space o k = Define the refractive index n of a dielectric medium as: o n = o o k = Waves in Dielectric Media Velocity A plane wave Has a dispersion relation given by ( ) r k j o e E n r E = E H...
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Lect16Isotropic - 1 ECE 3030 Electromagnetic Fields and...

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