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Unformatted text preview: Electromagnetics Workshop – Week 11 Solutions Dielectric Breakdown & Stored Energy Problem 1: Dielectric breakdown occurs in a material whenever the magnitude of the field E exceeds the dielectric strength anywhere in the material. a) In a coaxial capacitor filled with insulating material of permittivity ε , at what value of ρ is E a maximum? b) What is the breakdown voltage if 1 a = [cm], 2 b = [cm], and the dielectric material is mica with 6 r ε = and [ ] 200 MV/m BR = E ? c) If 24 V = [V], what is the energy stored per unit length in this coaxial capacitor? Problem 1 Solution: a) From Gauss’s Law, we can easily show that 2 E ρ ρ π ε ρ =  l Hence, E is a maximum when a ρ = . b) ( 29 ln ln 2 2 2 12 b a b V d a ρ ρ ρ ρ π ε ρ π ε π ε = = = ÷ ∫ l l l 12 2 BR BR E E a a ρ ρ π ε π ε = ⇒ = l l ( 29 ( 29 ( 29 ( 29 6 2 12 ln 2 ln 2 200 10 1 10 ln 2 1.386 MV 12 BR BR BR E a V E a π ε π ε = = = × × ≈ c) ( 29 ( 29 288 ln 2 24 12 ln 2 V π ε ρ ρ π ε = = ⇒ = l l , ( 29 24 ln 2 E ρ ρ =  ( 29 ( 29 2 2 2 0 0 6 3456 24 2 2 ln 2 ln 2 L b e V a L W dV d d dz π ε π ε ε ρ ρ φ ρ = = = ÷ ÷ ∫∫∫ ∫ ∫ ∫ E ( 29 [ ] 3456 / 138.7 nJ/m ln 2 e W L π ε = ≈ 1 Electromagnetics Workshop – Week 11 Solutions Dielectric Breakdown & Stored Energy Problem 2: A typical thundercloud can be modeled as a capacitor with horizontal plates with 10 [km 2 ] area separated by a vertical distance of 5 [km]. separated by a vertical distance of 5 [km]....
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 Spring '08
 Staff
 Electrostatics, Electromagnet, Electric charge, dielectric breakdown, eρ, Electromagnetics Workshop

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