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Unformatted text preview: Prof. David R. Jackson ECE Dept. Spring 2011 Notes 22 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism Uniqueness Theorem Uniqueness Theorem ( 29 , , x y z Given: is unique 2 v B =  = inside (known charge density) on boundary (known B.C.) Note: We can guess the solution, as long as we verify that the Poisson equation and the BCs are correctly satisfied! ( 29 , , ( ) v x y z known B = on boundary S Example Example v = Guess: B = V = constant Check: Hollow PEC shell Prove that E = 0 inside a hollow PEC shell (Faraday cage effect). ( 29 ( 29 , , x y z V r V = ( 29 2 2 in on S V V V = = = Therefore: The correct solution is V ( 29 , , x y z V = S Its the only solution that will satisfy both the BCs and the zero charge density requirement. Example (cont.) Example (cont.) v = Hollow PEC shell V ( 29 , , x y z V = S Hence E = everywhere inside the hollow cavity. ( 29 , , E x y z V =  =  = B = V = constant Image Theory Image Theory Note: The electric field is zero below the ground plane ( z < ). x z h ( x,y,z ) q = 0 infinite PEC ground plane This can be justified by the uniqueness theorem, just as we did for the Faraday cage discussion (make a closed surface by adding a large hemisphere in the lower region). Image Theory (cont.) Image Theory (cont.) Image picture: Note: There is no ground plane in the image picture!image picture!...
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This note was uploaded on 08/05/2011 for the course ECE 2317 taught by Professor Staff during the Spring '08 term at University of Houston.
 Spring '08
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