Notes+9+fall+2004

Notes+9+fall+2004 - Notes 9 fall 2004.doc Conductive...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Notes 9 fall 2004.doc Conductive materials Ampere’s law in free space: E j H o G G G ωε = × In a conductive medium it becomes: ( ) E j E E j j H G G G G G ε′ ω + ε ′ ω = ε ′ ε′ ω = × Alternatively we’ve written it as E j E J J H d c G G G G G G ε′ ω + σ = + = × Comparing the first terms of the last two equations we can see that ε′ ω = σ , or ω σ = ε ′ We can then write the permittivity for conductive media as ω σ ε′ = ε′ ε′ = ε j j . Dividing the boxed equation by we find the loss tangent that we mentioned earlier: ε′ tangent loss ε′ ω σ = ε′ ε′ Note that the ratio of the magnitudes of the phasor conduction current density to the phasor displacement current density is ° ε′ ω σ = ε′ ω σ = ε′ ω σ = 90 J J j E j E J J d c d c which shows that the displacement current density leads the conduction current density by (think ICE) ° 90 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Notes 9 fall 2004.doc Slightly conducting media We can make a useful approximation if we recall that for 1 x << , . The approximation gets better as x gets smaller (try it yourself). () nx 1 n x 1 ± ± A slightly conducting medium is defined by a loss tangent that is much less than one, i.e., 1 << ε′ ω σ or . In this case the complex propagation constant, , can be c d J J >> jk approximated by () () ε′ µ ω + ε′ µ σ = ε′ µ ω + ε′ ω ε′ µ ωσ = ε′ ω σ ε′ µ ω ε′ ω σ ε′ µ ω = ε′ µ ω = ε′ ε′ µ ω = µε ω = ω
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/20/2012 for the course EE 4460 taught by Professor Czarnecki during the Fall '10 term at LSU.

Page1 / 5

Notes+9+fall+2004 - Notes 9 fall 2004.doc Conductive...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online