EE325_quiz_3_sol_Yilmaz

EE325_quiz_3_sol_Yilmaz - NAME: _ Solution EE325-Fall 2009...

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NAME: _____________ Solution I EE325-Fall 2009 Quiz 3 1) Given the field 2 ˆˆ 6s i n 3c o s C / m ρφ ρ φ =+ Da a , evaluate the total charge in the region 2, 0 5 z ρ ≤≤ , and 0 φπ . (Hint: 11 () z D D D z D φ ρ ρ ρρ ρ φ ∇= + + ∂∂ i ) (5 points) 2 2 2 52 2 2 0 000 0 0 0 2 o s (6 sin ) (3 cos ) 12sin 3sin 9sin 45 sin 45 sin 180 2 vv v V Qd v ddd z dd d a D D C/m ( [Gauss' law in point form]) C ππ π ρ φ φφ φρ ρ ρ ρ φρ ρ φ φ ρ ρ φ φ φ + =− == = = = = ∫∫∫ i i ±²²²³²²²´ 2) Let 3 34 x y x yz Ga a . Given an initial point (2,1,1) and a final point (4,3,1), find d GL i using the parabolic path 2 62 , 1 y xz = . (5 points) (4,3,1) 3 (2,1,1) (4,3,1) 32 (2,1,1) 44 22 33 4 2 42 2 (3 4 ) ( ) 3 4 ; along the path 6 2, 1, 2 3( ) ) 66 92 2 1 46 94 2 2 2 6 xyxyz d xy z dx dy dz xy dx zdy y x z dy xdx xx x xdx x xdx x x a a a a a =++ + = + = = ++ + ∫∫ ii 4 9 21(4 2 ) (3 1) 21(4 2 ) 180 252 432 4 +− = + = EE325-Fall 2009 Quiz 3 1) Given the field 2 i n o s C / m a evaluate the electric flux S d DS i v leaving the closed region 2, 0 5 z ρ =≤
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This note was uploaded on 02/07/2010 for the course EE 325 taught by Professor Brown during the Fall '08 term at University of Texas at Austin.

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EE325_quiz_3_sol_Yilmaz - NAME: _ Solution EE325-Fall 2009...

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