notes12 2317 - ECE 2317 Applied Electricity and Magnetism...

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Prof. Filippo Capolino ECE Dept. Fall 2006 Notes 12 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)
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Example Example y x 0 B s ρ 0 A s x = - d/ 2 x = d/ 2 (a) x > d/ 2 00 22 A B ss x E ε =+ (c) x < -d/ 2 (b) -d/ 2 < x <d/ 2 AB x E =− A B x E
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Example (cont.) Example (cont.) y x x = - d/ 2 x = d/ 2 (a) x > d/ 2 0 x E = (c) x < - d/ 2 (b) -d/ 2 < x < d/ 2 0 0 s x E ρ ε = 0 x E = Choose: 00 0 0 AB s ss s ρρ = =− 0 s 0 s
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Example (cont.) Example (cont.) 0 0 s x E ρ ε = -d/ 2 < x < d/ 2 ideal parallel-plate capacitor 0 s 0 s y x h
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Perfect Electric Conductors (PEC) Perfect Electric Conductors (PEC) σ [S/m] J E = →∞ A B 0 B AB A VE d r = ⋅= PEC: Also, constant Φ = 0 E = since (Ohm’s law)
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Perfect Electric Conductors (PEC) Perfect Electric Conductors (PEC) Inside PEC: Proof: assume point where ρ v > 0 v = 0 Only s on the surface is allowed S v > 0 inside small volume ± 00 encl S encl Dnd S Q Q ⋅= => v Contradiction ! + + + + + + +
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Perfect Electric Conductors (PEC) Perfect Electric Conductors (PEC) Inside of a hollow PEC shell there is no electric field Only ρ s on the outer surface is allowed PEC shell + + + + + + + + + + + + E = 0 + “Faraday-cage effect”:
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Perfect Electric Conductors (PEC) Perfect Electric Conductors (PEC) Proof: Assume an electric field exits inside the shell at some point
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notes12 2317 - ECE 2317 Applied Electricity and Magnetism...

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