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notes11 2317

notes11 2317 - ECE 2317 ECE Applied Electricity and...

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Prof. David R. Jackson ECE Dept. Spring 2011 Notes 11 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism

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Example Example Assume ( 29 ˆ D D ρ ρ ρ = infinite uniform line charge ˆ encl S D n dS Q = Ñ x y z S ρ l = ρ l 0 [C/ m] h r Find the electric field vector
Example (cont.) Example (cont.) ( 29 ( 29 ( 29 ( 29 0 ˆ ˆ ˆ ˆ ˆ ˆ ˆ c t b encl l S S S S Q h D n dS D dS D z dS D z dS ρ ρ ρ ρ ρ ρ ρ ρ = = + + ⋅ - Ñ h S t S b S c ρ r

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Example (cont.) Example (cont.) ( 29 ( 29 0 0 ˆ 2 2 2 c c S S S l l D n dS D dS D dS D h D h h D ρ ρ ρ ρ ρ πρ πρ ρ ρ πρ = = = = = Ñ Hence So [ ] 0 0 V/m ˆ 2 l E ρ ρ πε ρ =
Example Example x y z ρ l 0 -h h When Gauss’s Law is not useful ˆ ˆ encl S D ndS Q D D ρ ρ = Ñ E has more than one component ! E is not a function of only ρ !

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Example Example ρ v = 3 ρ 2 [C/m3] , ρ < a Assume ( 29 ˆ D D ρ ρ ρ = non-uniform infinite cylinder of volume charge density ˆ encl S D n dS Q = Ñ x y z S h a ρ r Find the electric field vector everywhere
Example (cont.)

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notes11 2317 - ECE 2317 ECE Applied Electricity and...

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