notes14 2317 - Potential Calculation ECE 2317 Applied...

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Prof. Filippo Capolino ECE Dept. Fall 2006 Notes 14 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) Hence: Potential Calculation Potential Calculation () B AB A VE d r A B =⋅ −Φ r R Rr E d r Φ− Φ=⋅ r R rR E d r Φ= Φ −⋅ C r = B R = A Example Example Given: R = , Φ ( R ) = 0 2 0 4 q Er r πε ⎛⎞ = ⎜⎟ ⎝⎠ ± Choose a radial path for convenience Find the potential function y z q r R C r R E d r Φ 0 r R E dr Φ= − Example (cont.) Example (cont.) ± ± 2 0 0 sin 4 4 r r R r r R r r rE rdr rd r d Ed r q dr r q r ±± θ θφ Φ=− + + =− = [] 0 V 4 q r r
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Example Example Given: R is at ρ = b, Φ ( R ) = 0 l 0 0 2 E περ ⎛⎞ = ⎜⎟ ⎝⎠ A Find the potential function Choose a radial path x y z l 0 [C/m] r R ( =b ) C () l l ± 0 r R r R b Ed r E dz d z d ρρ φρφ Φ= =− + + ± Example (cont.) Example (cont.) 0 0 0 0 0 0 2 ln 2 ln 2 b b d b A A A πε ρ πε
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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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notes14 2317 - Potential Calculation ECE 2317 Applied...

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