329sum09hw4sol

# 329sum09hw4sol - ECE-329 Summer 2009 Homework 4 —...

This preview shows pages 1–2. 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: ECE-329 Summer 2009 Homework 4 — Solution June 25, 2009 1. For E = 2ˆ x + z ˆ y V / m , we have that ∇ × E = ˆ x ˆ y ˆ z ∂ ∂x ∂ ∂y ∂ ∂z 2 z = 1ˆ x. Then, since ∇ × E 6 = , field E is not electrostatic. 2. A vacuum diode consists of a cathode in the x = 0 plane and an anode in the x = d plane. The potential distribution between the plates is given by V ( x ) = V a ( x/d ) 4 / 3 where V a = 1 V . a) The electric field between the plates is E =-∇ Φ =- 4 3 d x d 1 / 3 ˆ x V m . Evaluating at x = d 2 , we get E ( x = d 2 ) =- 2 5 / 3 3 d ˆ x V m . b) The volumetric free-charge density is ρ = ∇ · D = ∇ · ( o E ) =- 4 o 9 d 2 d x 2 / 3 C m 3 . Evaluating at x = d 4 , we get ρ ( x = d 4 ) =- 4 5 / 3 o 9 d 2 C m 3 . c) The surface charge density on the anode (where ˆ n =- ˆ x ) is ρ S = D · ˆ n | x = d =- D x | x = d = 4 o 3 d C m 2 . 3. Consider a pair of parallel conducting plates placed at z = 0 and z = W that sustains an electric field E = 3ˆ z V / m . The gap between the plates is originally occupied by vacuum ( o , μ o ). a) In free space D = o E , then the displacement field between the plates is D = 3 o ˆ z C m 2 . By definition, D = o E + P , thus the polarization field between the plates is P = C m 2 ....
View Full Document

## This note was uploaded on 09/16/2011 for the course ECE 329 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.

### Page1 / 4

329sum09hw4sol - ECE-329 Summer 2009 Homework 4 —...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online