329fall08hw2sol - ECE-329 Fall 2008 Homework 2 (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 2008 Homework 2 (Solution) September 10, 2008 1. The infinitesimal electric field at position ( x o , , 0) generated by an infinite charge strip along the z-axis with an infinitesimal width dx is found to be d ~ E = ˆ x ρ S 2 π o x o dx, where ρ S is the uniform surface charge density. We can use this result to compute the electric field produced at the same location by a charge strip of finite width W that extends from x = 0 to x = W < x o (see the next figure). dx x z W d ~ E x o x o- x x Since the contribution of an infinitesimal strip that is placed at a distance x from the origin is simply d ~ E = ˆ x ρ S 2 π o ( x o- x ) dx, the total field produced by the strip can be easily obtained by integrating d ~ E from x = 0 to x = W as follows ~ E = ˆ x W ˆ ρ S 2 π o ( x o- x ) dx = ˆ x ρ S 2 π o [- ln( x o- x )] W = ˆ x ρ S 2 π o (- ln( x o- W ) + ln( x o )) = ˆ x ρ S 2 π o ln x o x o- W . 1 ECE-329 Fall 2008 2. We will apply Gauss law ˛ S ~ E · d ~ S = 1 o ˆ V ρdV to compute the electric flux ¸ S ~ E · d ~ S over the surface of a cube of volume V = L 3 that is centered at the origin. L 2 (1 , 1 , 1) L 2 (- 1 , 1 , 1) L 2 (- 1 , 1 ,- 1) L 2 (1 , 1 ,- 1) L 2 (1 ,- 1 ,- 1) L 2 (1 ,- 1 , 1) L 2 (- 1 ,- 1 , 1) L 2 (- 1 ,- 1 ,- 1) x y z d ~ S 2 d ~ S 1 d ~ S 3 (a) If the electric charge density within the cube is ρ = 1 C / m 3 , the total electric flux can be computed as follows ˛ S ~ E · d ~ S = 1 o ˆ V ρdV = 1 o ˆ V dV = 1 o L/ 2 ˆ- L/ 2 dx L/ 2 ˆ- L/ 2 dy L/ 2 ˆ- L/ 2 dz = L 3 o V · m ....
View Full Document

This note was uploaded on 04/14/2009 for the course ECE 329 taught by Professor Franke during the Spring '08 term at University of Illinois at Urbana–Champaign.

Page1 / 7

329fall08hw2sol - ECE-329 Fall 2008 Homework 2 (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