329fall10hw3sol

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

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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 ) = &quot; ( 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 ....
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## 329fall10hw3sol - ECE 329 Fall 2010 Homework 3 - Solution...

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