notes15 2317 - ECE 2317 Applied Electricity and Magnetism...

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Prof. Filippo Capolino ECE Dept. Fall 2006 Notes 15 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism Notes prepared by the EM group, University of Houston . (used by Dr. Jackson, spring 2006) Potential Integral Formula Potential Integral Formula This is a method for calculating the potential function directly, without having to calculate the electric field first. This is often the easiest way to find the potential function (especially when you don’t already have the electric field calculated) The method assumes that the potential is zero at infinity. (If this is not so, you must remember to add a constant to the solution.) Potential Integral Formula (cont.) Potential Integral Formula (cont.) x y z ρ v ( r ´ ) r ( x , y , z ) R r ´ ( ) 0 Φ∞= () 00 '' 44 v rd V dQ d R R πε Φ= = 0 ,0 4 v V V r R Φ = Integrating,we obtain the following result: Potential Integral Formula (cont.) Potential Integral Formula (cont.) Similarly 0 0 4 4 s S C S r R l r R A
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Example Example Find Φ ( 0, 0, z ) ( ) 0 Φ∞= () 0 0 22 2 0 0 0 0 0 4 4 2 4 C d r R
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This note was uploaded on 10/25/2011 for the course ECE 2317 taught by Professor Staff during the Fall '08 term at University of Houston.

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notes15 2317 - ECE 2317 Applied Electricity and Magnetism...

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