notes14 2317

# notes14 2317 - ECE 2317 ECE Applied Electricity and...

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Prof. David R. Jackson ECE Dept. Spring 2011 Notes 14 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism

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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 0 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 - 0 r R E dr Φ = - y z q r R C point charge x

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Example (cont.) Example (cont.) ( 29 ( 29 2 0 0 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 [ ] 0 V 4 q r r π ε Φ =
Example (cont.) Example (cont.) ( 29 ( 29 2 0 0 0 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 ? y z q r R C point charge x The answer would not change! By superposition, the potential from any set of charges is path independent in statics.

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