329fall10hw3sol - ECE 329 Fall 2010 Homework 3 - Solution...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE 329 Fall 2010 Homework 3 - Solution Due: Sept. 14, 2010 1. E =- V = x x + y y + z z ( xz 2 ) =- z 2 x- 2 xz z, = D = ( E ) = ( E ) = x x + y y + z z (- x z 2- z 2 xz ) =- 2 x. 2. According to the relationship between electric eld and potential, we have V (0 , , 0)- V ( x,y,z ) = ( x,y,z ) (0 , , 0) E d l = ( x,y,z ) (0 , , 0) ( x x + y y- 4 z ) ( xdx + ydy + zdz ) = ( x,y,z ) (0 , , 0) ( x dx + y dy- 4 dz ) . Since E = x y z x y z x y- 4 = 0 , the integration above is path-indepent and we can simply choose three segments along x, y and z directions, respectively. Here, we choose the integral path as (0 , , 0) to ( x, , 0) , ( x, , 0) to ( x,y, 0) , and ( x,y, 0) to ( x,y,z ) . Accordingly, V (0 , , 0)- V ( x,y,z ) = " ( x, , 0) (0 , , 0) + ( x,y, 0) ( x, , 0) + ( x,y,z ) ( x,y, 0) # ( x dx + y dy- 4 dz ) = ( x, , 0) (0 , , 0) x dx + ( x,y, 0) ( x, , 0) y dy- ( x,y,z ) ( x,y, 0) 4 dz = x 2 2 + y 2 2- 4 z. Since V (0 , , 0) = 0 , we obtain V ( x,y,z ) =- x 2 2- y 2 2 + 4 z ( V ) . 1 ECE 329 Fall 2010 3. a) We can write E as E = Q 4 x x r 3 + y y r 3 + z z r 3 ....
View Full Document

Page1 / 5

329fall10hw3sol - ECE 329 Fall 2010 Homework 3 - Solution...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online