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ECE-305 Test1 Review

# ECE-305 Test1 Review - Engineering Electro-Magnetics...

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Engineering Electro-Magnetics Engineering Electro-Magnetics ECE-305, Test 1 Review Dennis McCaughey, Ph.D. 23 February 2010

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02/23/2010 Dennis McCaughey, ECE305, Spring 2010 2 Example 3.5 (Divergence Theorem) Example 3.5 (Divergence Theorem) x y z x =1 y =2 z =3 2 xy a x 2 x 2 a y 2 2 has no component 0 on the surfaces: x y xya x a z d = + = D D D S { } { } , , 0 1, 0 2, 0 and , , 0 1, 0 2, 3 x y z x y z x y z x y z = = ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 3 2 3 2 0 0 0 0 3 2 3 2 0 0 0 0 3 2 0 0 Surfaces in the plane 0, , 1, , 0 2 2 3 0 4 0 Surfaces in the plane 12 x x x x S x x x x yz d dz dy y z a dz dy y z a dz dy a a dz dy ya a dz dy y xz d = - + = - + = = - = - D S D D D Ñ ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 3 1 3 1 0 0 0 0 3 1 3 1 2 2 0 0 0 0 ,0, 2 0 , , y y y y S y y y y dz dx x z a dz dx x z a dz dx x a a dz dx x a a = - + = - + = S D D Ñ
02/23/2010 Dennis McCaughey, ECE305, Spring 2010 3 Example 3.5 Continued Example 3.5 Continued ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 3 2 1 0 0 0 2 2 2 0 = 2 3 0 4 0 1 0 12 x y v xya x a xy x y x y dz dy y dx = = + ∇• = + = + ∇• = - - - D D D

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02/23/2010 Dennis McCaughey, ECE305, Spring 2010 4 Homework Solutions Homework Solutions
02/23/2010 Dennis McCaughey, ECE305, Spring 2010 5 Homework Solutions Homework Solutions

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02/23/2010 Dennis McCaughey, ECE305, Spring 2010 6 Solutions Solutions
02/23/2010 Dennis McCaughey, ECE305, Spring 2010 7 Solutions Solutions

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02/23/2010 Dennis McCaughey, ECE305, Spring 2010 8 Solutions Solutions
02/23/2010 Dennis McCaughey, ECE305, Spring 2010 9 Solutions Solutions

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