EEE224_Fall10_Lecture2 - METU - NCC EEE 224 ELECTROMAGNETIC...

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1 EEE 224 ELECTROMAGNETIC THEORY Orthogonal Coordinate Systems METU - NCC Assist. Prof. Dr. Özlem Özgün Office : S-144 Phone : 661 2972 E-mail : ozozgun@metu.edu.tr Web : http://www.metu.edu.tr/~ozozgun/
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2 Coordinate Systems ± The physical quantities in EM are vector fields which are functions of space and time. To describe the variations of the quantities in space, we need a suitable coordinate system. ± Laws of electromagnetism are “invariant” with the chosen coordinate system. ± A point in 3D space can be specified as the intersection of 3 surfaces. u 1 = const. u 2 = const. u 3 = const. u’s may be lengths or angles. ± When these 3 families of surfaces are mutually orthogonal (perpendicular) to each other, we have an “orthogonal coordinate system”.
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3 Orthogonal Coordinate Systems 3 PRIMARY “ORTHOGONAL” COORDINATE SYSTEMS: CARTESIAN CYLINDRICAL SPHERICAL Choice is based on symmetry of problem Examples: Sheets - CARTESIAN Wires/Cables - CYLINDRICAL Spheres - SPHERICAL How do we choose a suitable coordinate system?
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4 Spherical Coordinates Cylindrical Coordinates Cartesian Coordinates P (x, y, z) P (R, θ , φ ) P (r, φ , z) x y z P(x,y,z) Φ z r x y z P(r, Φ , z) θ Φ R z y x P(R, θ , Φ ) Coordinate Systems Useful in problems having cylindrical symmetry Useful in problems having spherical symmetry Useful in problems having rectangular symmetry r
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5 Cartesian Coordinate System Coordinate variables (u 1 , u 2 , u 3 ) = (x, y, z) ,, x yz aaa Unit vectors: Ranges: a x always points in the direction of increasing x , and is orthogonal to the x -constant plane. Similarly, for a y and a z
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6 Cartesian Coordinate System
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This note was uploaded on 01/07/2011 for the course EE 209 taught by Professor Alexander during the Spring '10 term at Middle East Technical University.

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EEE224_Fall10_Lecture2 - METU - NCC EEE 224 ELECTROMAGNETIC...

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