lec3 - 1 2 2 1 2 12 12 12 ) ( ) ( ) ( z z y y x x d R R R...

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Lecture Notes for C-term 2009 Lecture 3 Prof. R. Ludwig Department of Electrical and Computer Engineering Worcester Polytechnic Institute Worcester, MA ECE 2112 Electromagnetic Theory Copyright, 2000 © R. Ludwig
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ECE2112_3 2 Lecture 3 Objectives • What is the generic representation of a vector? • How is a distance vector defined? • What is a dot product? • What is a cross product?
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ECE2112_3 3 ECE 2112 - Lecture 3 • Vector Algebra Description of a point in space is given by a vector z z y y x x A A A u u u A y y x z y x u u u R If A=R : position vector 2 2 2 z y x R distance Vector consists of unit vectors and vector components
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ECE2112_3 4 ECE 2112 - Lecture 3 • Distance between two points (source - receiver) ) ( ) ( ) ( 1 2 1 2 1 2 1 2 12 z z y y x x z y x u u u R R R 2 1 2 2
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Unformatted text preview: 1 2 2 1 2 12 12 12 ) ( ) ( ) ( z z y y x x d R R R Underlying feature of all field phenomena is the definition of source-receiver distance! ECE2112_3 5 Dot product (needed for electrostatics) Cross product (needed for magnetostatics) ECE 2112- Lecture 3 AB AB cos B A AB AB sin n B A ( exploits orthogonality) ECE2112_3 6 Cross product evaluation (method of Sarrus) ECE 2112- Lecture 3 ... ) ( x A B B A B B B A A A z y x z y z y z y x z y x B A | | | y x y x z y x z y x B B A A y x B B B A A A z y x B A...
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lec3 - 1 2 2 1 2 12 12 12 ) ( ) ( ) ( z z y y x x d R R R...

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