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1-29-08Lec07

# 1-29-08Lec07 - Lecture 7-1 Electric Potential Energy and...

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Lecture 7 Lecture 7 - 1 Electric Potential Energy and Electric Potential positive charge High U (potential energy) Low U negative charge High U Low U High V (potential) Low V Electric field direction High V Low V Electric field direction

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Lecture 7 Lecture 7 - 2 Potential due to two (source) charges 1 2 ( ) | | | | q q V x k k x x a = + 1 2 0 q q = >
Lecture 7 Lecture 7 - 3 E from V x V E x =− y V E y =− z V E z =− Expressed as a vector, E is the negative gradient of V V E = arrowrightnosp arrowrightnosp We can obtain the electric field E from the potential V by inverting the integral that computes V from E : ( ) ( ) r r x y z V r E dl E dx E dy E dz =− =− + + arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp i E always points from high V to low V. (But high V is high U only for a positive charge.)

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Lecture 7 Lecture 7 - 4 Equipotential Surfaces • An equipotential surface is a surface on which the potential is the same everywhere. 0 0 U V q Δ Δ = = For a displacement Δ r of a test charge q 0 along an equipotentital , 0 0 E E q U W r Δ =− = Δ = combarrowextenderarrowrightnosp arrowrightnosp i E an equipotential surface everywhere.
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1-29-08Lec07 - Lecture 7-1 Electric Potential Energy and...

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