aee1_2008_a01 - Prof. S. Peik AEE1 Assignment 1 Deadline:...

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AEE1 Assignment, Fall 2007 Prof. S. Peik AEE1 Assignment 1 Deadline: next Friday Prerequisite: calculus for several variables, cartesian, cylindrical and spherical coordinate systems, Some high school physics To be studied: Lecture Notes Chapter 1 Lecture Notes Appendix 12.1 -12.3.1 Sadiku Coordinate Systems Objectives of this Assignment: To get familiar with the application of basic calculus to elec- trostatic charge distributions, Understand the concept of charge, voltage, current and it’s basic relation Problem 1 2 3 4 Max. Points 11 - - - Points Total Points: of 11 Mark: Problem 1: A cylinder with radius R and length l is charged on its nappe surface with a surface charge of σ ( ρ , φ , z ) = σ 0 ( sin 2 φ ) (1) The bottom and top lid are charged with a constant surface charge density σ 0 . x y z nappe surface l R 1. Find the total charge of the top lid? 3 points 2. Find the total charge of the nappe? 6 points 3. Find the total charge of the cylinder? 2 points Hint: You may use an integral table to find R sin 2 x
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AEE1 Assignment, Fall 2007
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Unformatted text preview: Prof. S. Peik AEE1 Assignment 1 Deadline: next Friday Prerequisite: • calculus for several variables, • cartesian, cylindrical and spherical coordinate systems, • Some high school physics To be studied: • Lecture Notes Chapter 1 • Lecture Notes Appendix 12.1 -12.3.1 • Sadiku Coordinate Systems Objectives of this Assignment: • To get familiar with the application of basic calculus to elec-trostatic charge distributions, • Understand the concept of charge, voltage, current and it’s basic relation Problem 1 2 3 4 Max. Points 11---Points Total Points: of 11 Mark: Solution 1: 1) Q top = Q bot = π R 2 σ 2) Q nap = σ Z l 2-l 2 Z 2 π sin 2 ( φ ) Rd φ dz = σ l Z 2 π sin 2 ( φ ) Rd φ (1) = σ lR [ φ 2-π 4-sin 2 φ 4 ] 2 π = σ lR 2 π 2 (2) = σ l π R (3) 3) total Charge Q tot = 2 π R 2 σ + σ l π R = π R σ ( 2 R + l )...
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aee1_2008_a01 - Prof. S. Peik AEE1 Assignment 1 Deadline:...

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