ECE-305-Lecture4

ECE-305-Lecture4 - Engineering Electro-Magnetics Engineering

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Unformatted text preview: Engineering Electro-Magnetics Engineering Electro-Magnetics ECE-305, Lecture 4 Dennis McCaughey, Ph.D. 26 January 2010 01/26/2010 Dennis McCaughey, ECE305,Spring 2010 2 Homework Homework Problems 2.3 and 2.7 Due Next Tues February 2 01/26/2010 Dennis McCaughey, ECE305,Spring 2010 3 2.3 Field Due to a Continuous Volume 2.3 Field Due to a Continuous Volume Charge Distribution Charge Distribution Region filled with charges separated by minute distances Define a charge density, charge per unit volume The integral is a triple Difficult to evaluate in all but the most symmetrical problems 3 Charge Density: ( ) Small charge in a small volume: lim Total charge within some finite volume v v v V v vol C m Q V Q V Q dv = = = 01/26/2010 Dennis McCaughey, ECE305,Spring 2010 4 Example 2.3: Charge in an Electron Example 2.3: Charge in an Electron Beam Beam ( 29 5 5 5 0.04 2 0.01 6 10 0.02 0 0.04 0.01 5 10 0.02 0 .04 0.01 5 10 5 0.0 .02 0.01 10 2000 4000 2000 10 5 10 first 10 next 10 = 10 = 10 10 2000 v vol z z z z z Q dv e d d dz e d dz z e d e e d e e ---- =-- =------ = =- - - - -- = --- .01 4000 10 4000 1 1 10 0.0785 4000 2000 pC - - -- = Use cylindrical coordinates 01/26/2010 Dennis McCaughey, ECE305,Spring 2010 5 Example 2.3: Setup in Rectangular Example 2.3: Setup in Rectangular Coordinates Coordinates { } ( 29 2 2 5 , , 0.01,0.02 0.04 0.04 2 0.01 6 10 0.02 : 5 10 v vol v x y z x y z z Q dv dxdydz Jacobian dxdydz d d dz dz d d e + -- = = = =- 01/26/2010 Dennis McCaughey, ECE305,Spring 2010 6 Electron Beam Current Estimate...
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This note was uploaded on 09/13/2011 for the course ECE 305 taught by Professor Staff during the Spring '08 term at George Mason.

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ECE-305-Lecture4 - Engineering Electro-Magnetics Engineering

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