notes20 2317 - ECE 2317 Applied Electricity and Magnetism...

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Prof. Filippo Capolino ECE Dept. Fall 2006 Notes 20 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism Notes prepared by the EM group, University of Houston . (used by Dr. Jackson, spring 2006) Boundary Conditions for Dielectrics Boundary Conditions for Dielectrics z ε 1 ε 2 Tangential component of electric field: A E x1 B E x2 x 1 2 0: AB x AB x z VE x z x + =≈ Δ Δ 12 x x E E = Hence tt E E = In general, Δ x Boundary Conditions (cont.) Boundary Conditions (cont.) ε 1 ε 2 Normal Component: E z 1 + + + + + + + + + + + ρ s E z 2 Gauss’ Law: ± encl S D nds Q ⋅= v z S (“pill box”) Δ S + + + + + + + + + + + zz s s nn s D SD S S DD Δ− Δ= Δ −= ± n points toward region 1 In general, Boundary Conditions (cont.) Boundary Conditions (cont.) ± () s nD D ⋅− =
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Example Example ε top = 2 ε 0 Find ρ s z ε bot = 3 ε 0 ± ± ± ± 234 233 top bot E xyz E =−+ =−− ± ± choose ± nz = ± z ± n 1 2 + + + + + + + + + + + + + + + (This establishes which region is region 1.) Example (cont.) Example (cont.) () ± () () ( ) 12 00 24 3 3 s top bot s top top bot bot sr z r z DDn DDz EE ρ ρε
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This note was uploaded on 10/25/2011 for the course ECE 2317 taught by Professor Staff during the Fall '08 term at University of Houston.

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notes20 2317 - ECE 2317 Applied Electricity and Magnetism...

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