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

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