notes19 2317

notes19 2317 - ECE 2317 Applied Electricity and Magnetism...

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Prof. Filippo Capolino ECE Dept. Fall 2006 Notes 19 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) Dielectric Breakdown Dielectric Breakdown 1 Arcing (spark) E c = “critical electric field” (air ionizes) Air Oil Glass [ ] [] 6 6 6 31 0 V /m 15 10 V/m 30 10 V/m c c c E E E + - E x E x = E c x Dielectric Breakdown (cont.) Dielectric Breakdown (cont.) 2 Corona Discharge (local breakdown) + - E > E c Power line Lines are sometimes grouped to reduce losses and corona effect. Example Example coaxial cable a b r ε 6 2.0 15 10 [V/m] 0.25 cm 0.5 mm r c E b a = = = Find: V max (assume a safety factor SF = 2 ) l max 0 max 0 2 2 r c r E a E a ρ πεερ πε ε ⎛⎞ = ⎜⎟ ⎝⎠ = = A A Set l max - l max + + + + + + - - - - - -
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Example (cont.) Example (cont.) Thus max 0 2 rc aE ρπ ε = A l l max 0 max 2 ln c r B b AB Aa b c a b c a a EE VV E d r E d a Ed Ea A ρ ρρ πεερ ⎛⎞ == ⎜⎟ ⎝⎠ ==⋅ = = = ∫∫ Hence or max ln c b VE a a = Example Example With safety factor: () max 63 1 ln 1 15 10 0.5 10 ln 5 2 SF c b a SF a = =×× [] max 6035.4 SF = Van de Graaff Generator Van de Graaff Generator Electric field is high near sharp points: charges are free to jump on/off Faraday cage effect: no matter how much charge is placed on the dome, it goes to the outside and there is little field on the inside Principles: Dr. Robert J. Van de Graaff (1901-1967) was a professor at Princeton university and a Research Associate at MIT. The Van de Graaff generator was invented in 1929 and originally used as a research tool in early atom-smashing and high energy X-ray experiments. Van de Graaff Generator (cont.) Van de Graaff Generator (cont.)
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Van de Graaff Generator (cont.) Van de Graaff Generator (cont.) This picture shows Dr. Van de Graaff with his first generator (80 [kV]).
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notes19 2317 - ECE 2317 Applied Electricity and Magnetism...

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