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**Unformatted text preview: **ECE 3030: Electromagnetic Fields and Waves Fall 2009 DEMO 2 INSTRUCTOR NOTES: Electric Fields Produced by Charges Reminder: Key item: Separation of Variables. Date: Tuesday 9/8 1. Vector fields versus position vectors. Vector fields in the three co- ordinate systems are written as: ~ A = A x ( x, y, z )x + A y ( x, y, z )y + A z ( x, y, z ) z ~ A = A r ( r, , z ) r + A ( r, , z ) + A z ( r, , z ) z ~ A = A r ( r, , ) r + A ( r, , ) + A ( r, , ) Now ask your class: How are position vectors written in the three coordinate systems? Make sure you wait for some answers from your class on each of these. This is subtle if you have never been through this before. Cartesian: ~ r( x, y, z ) =? (= x x + y y + z z) The students should get this one. Cylindrical: ~ r( r, , z ) =? ( not = r r + + z z , but = r r( ) + z z ) Spherical: ~ r( r, , ) =? ( not = r r + + , but = r r( , ) ) 2. Review Boundary Conditions (B.C.): ( ) = 0 ~ E k is continuous (the same) on either side of a boundary. ~ D = ~ E is continuous across boundaries. For perfect conductors ~ E k = 0 which means ~ E is perpendicular at the boundary, i.e., ~ E = ~ E just outside the conductor. Equipotential surfaces (including perfect conductor surfaces) are al- ways to ~ E lines. These concepts often allow decent graphical analysis. Example: Sketch field and equipotential lines between two charged potatoes...develop from spherical shells. 3. Again note importance of drawing good figures! CORNELL UNIVERSITY c WES SWARTZ (09/8/10; R09/9/5) 21 ECE 3030: Electromagnetic Fields and Waves Fall 2009 DEMO 2 INSTRUCTOR NOTES: Electric Fields Produced by Charges 4. Separation of Variables will not be covered in lecture, so cover basics here so that they understand the MatLab programs that will apply the technique. You may want to review Section 3.6 in the text, some of which is abstracted here....

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