notes14 2317 - Prof David R Jackson ECE Dept Spring 2011...

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Unformatted text preview: Prof. David R. Jackson ECE Dept. Spring 2011 Notes 14 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism Hence: Potential Calculation Potential Calculation ( 29 ( 29 B AB A V E dr A B ≡ ⋅ = Φ- Φ ∫ ( 29 ( 29 R r r R E dr Φ- Φ = ⋅ ∫ ( 29 ( 29 r R r R E dr Φ = Φ- ⋅ ∫ C r = A R = B Example Example Given: R = ∞ , Φ ( R ) = 0 2 ˆ 4 q E r r π ε = Choose a radial path for convenience. Find the potential function ( 29 ( 29 r R r R E dr Φ = Φ- ⋅ ∫ r R E dr Φ =- ⋅ ∫ y z q r R C point charge x Example (cont.) Example (cont.) ( 29 ( 29 2 ˆ ˆ ˆ ˆ sin 4 4 r r R r r R r r r E r dr r d r d E dr q dr r q r θ θ φ θ φ π ε π ε ∞ ∞ Φ = - ⋅ + + = - = - = ∫ ∫ ∫ ( 29 [ ] V 4 q r r π ε Φ = Example (cont.) Example (cont.) ( 29 ( 29 2 ˆ ˆ ˆ ˆ sin 4 4 4 r r R r r R r r r E r dr r d r d E dr q dr r q r q r θ θ φ θ φ π ε π ε π ε ∞ ∞ Φ = - ⋅ + + = - = - = = ∫ ∫ ∫ What if we had picked a different path C ?...
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This note was uploaded on 08/05/2011 for the course ECE 2317 taught by Professor Staff during the Spring '08 term at University of Houston.

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notes14 2317 - Prof David R Jackson ECE Dept Spring 2011...

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