aee1_2008_a04 - AEE1 Assignment 4 Fall 2008 Prof S Peik...

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Unformatted text preview: AEE1 Assignment 4, Fall 2008 Prof. S. Peik AEE1 Assignment 4 Deadline: next Wednesday Name: ______________________________________ Prerequisite: Electrical Fields Charge Distributions cartesian, cylindrical and spherical coordinate systems, To be studied: Lecture Notes Chapter 3 Sadiku Coordinate Systems 4.7 and 4.8 Ulaby 4.5 Griffiths 2.3 and 2.4 Objectives of this Assignment: To get more familiar with vector fields Understanding conservative fields Problem 1: An E-field is perpendicular to the xy-plane everywhere in space as shown. The E-field increases linearly with x. The field magnitude at the origin is V |E1 (0, 0, 0)| = E0 = 10 m . z P1 P3 P2 y x E 1. Find the equation for the E-Field vector E1 (x, y, z). Use the notation with unit vectors, e.g. x, y,and z. ^ ^ ^ 2. Find the work performed, when moving a charge of 1 C from the origin to the point P3 = (1m, 0, 1m). Use the Path Origin-P1-P3. 3. Find the work performed, when moving a charge of 1 C from the origin to the point P3 = (1m, 0, 1m). Use the Path Origin-P2-P3. 4. Is the E-Field conservative? 5. Can we find a unique potential field? Problem Max. Points Points 1 14 2 - 3 - 4 - Total Points: Points: 6. We superimpose a second E-field E2 = E0 zx to the original field. Repeat ^ step 2 to 5 on the total field E = E1 + E2 of 14 7. Write down the potential field of 6. assuming V (0, 0, 0) = 0V. Hint: We cannot proof the existance of a unique V -Field yet. Assume your two tests are sufficient as a proof. AEE1 Assignment 4, Fall 2008 Prof. S. Peik AEE1 Assignment 4 Deadline: next Wednesday Name: ______________________________________ Prerequisite: Electrical Fields Charge Distributions cartesian, cylindrical and spherical coordinate systems, To be studied: Lecture Notes Chapter 3 Sadiku Coordinate Systems 4.7 and 4.8 Ulaby 4.5 Griffiths 2.3 and 2.4 Objectives of this Assignment: To get more familiar with vector fields Understanding conservative fields Solution 1: 1. E1 = -E0 (x + 1)^ z 2. W = Q E dl since P2-P3 is perpendicular to the field, this work is zero hence W0-P1-P3 = QE0 1m = 10J 3. similar W0-P2-P3 = QE0 2 1m = 20J 4. Work is not independent of path -not conservative 5. No scalar potential possible 6. E = E0 (x + 1)^ + E0 zx z ^ W0-P1 = 10J R P1 0 P1 R Q [E0 (x + 1)^ + E0 zx] zdz = Q z ^ ^ R z=1 z=0 x=0 E0 (x + 1)dz E0 zdx x=0 = QE0 1m = WP1-P3 = R P3 Q [E0 (x + 1)^ + E0 zx] xdx = Q z ^ ^ R x=1 z=1 = QE0 1m = 10J W0-P1-P3 = W0-P1 +WP1-P3 = 20J W0-P2 = R P2 0 Q [E0 (x + 1)^ + E0 zx] xdx = Q z ^ ^ R x=1 x=0 E0 zdx z=0 = 0dx = 0 = QE0 2 R WP2-P3 = 1m = 20J Problem Max. Points Points 1 14 2 3 4 Total Points: Points: 7. of 14 R P3 P2 Q [E0 (x + 1)^ + E0 zx] zdz = Q z ^ ^ R z=1 z=0 E0 (x + 1)dz x=1 W0-P2-P3 = W0-P1 +WP1-P3 = 20J seems to be OK, but no proof! AEE1 Assignment 4, Fall 2008 Prof. S. Peik V = Z x 0 E0 zdx z=0 + Z z=1 z=0 E0 (x + 1)dz x=x (1) (2) = 0+ Z z=1 z=0 E0 (x + 1)dz x=x = E0 (x + 1) (3) ...
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This note was uploaded on 05/04/2010 for the course EECS 320256 taught by Professor Peik during the Fall '09 term at Jacobs University Bremen.

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