ECE-305-Lecture5 - Engineering Electro-Magnetics...

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Engineering Electro-Magnetics Engineering Electro-Magnetics ECE-305, Lecture 5 Dennis McCaughey, Ph.D. 28 January 2010
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01/28/2010 Dennis McCaughey, ECE305, Spring 2010 2 Streamlines Streamlines Everywhere tangent to E Arrows indicate direction In some important cases the field intensity can be indicated by the inverse proporionality of the spacing between the streamlines A line every 45 0 indicates azimuthal symmetry
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01/28/2010 Dennis McCaughey, ECE305, Spring 2010 3 Streamlines Streamlines 0 2 2 2 2 Let 0 Example: Uniform line charge 2 1 ln ln z y x L x y y x E E dy E dx a x y a a x y x y E dy y dy dx E dx x y x y x C y Cx ρ ρ πε ρ = = = = = + + + = = = + = E
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01/28/2010 Dennis McCaughey, ECE305, Spring 2010 4 Drill D 2.7 a Drill D 2.7 a ( 29 ( 29 2 2 2 2 2 2 2 2 2 1,4, 2 8 4 4 1 8 2 2 2 1 2 4 33 2 33 x y P x x a a y y dy x y x dx y x y ydy xdx x y C C x y = - - = + = = - - = - + = = + = + = E
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01/28/2010 Dennis McCaughey, ECE305, Spring 2010 5 Electric Flux Density Electric Flux Density Faraday’s Experiment Setup 2 concentric sets metal hemispheres that could be clamped together 2 concentric dielectric (insulating) hemispheric shells that filled the volume between the two outer metal hemispheres
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