Week 11 Solns

# Week 11 Solns - Electromagnetics Workshop – Week 11...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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]....
View Full Document

## This note was uploaded on 10/25/2011 for the course ECE 2317 taught by Professor Staff during the Spring '08 term at University of Houston.

### Page1 / 5

Week 11 Solns - Electromagnetics Workshop – Week 11...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online