Lecture 11

# Lecture 11 - Potential at a Certain Location 1 Add up the...

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1. Add up the contribution of all point charges at this point V A = 1 4 πε 0 q i r i i q 1 r 1 q 2 r 2 A 2. Travel along a path from point very far away to the location of interest and add up at each step: E d l V A = E d l A q 1 q 2 E dl Potential at a Certain Location

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1. Subtract the potential at the initial location A from the potential at final location B Δ V = V B V A 2. Travel along a path from A to B adding up at each step: l d E Δ V = E d l A B A B B E dl Finding Potential Difference
A Example: E = 0 inside a charged metal sphere, but V is not! Common Pitfall Assume that the potential V at a location is defined by the electric field at this location. E

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Electric field in capacitor filled with insulator: E net = E plates +E dipoles E plates = const (in capacitor) 1 2 3 4 5 E dipoles,A A B E dipoles,B E dipoles =f(x,y,z) Travel from A to B : E dipoles is sometimes parallel to dl , and sometimes antiparallel to dl = Δ B A l d E V Potential Difference in an Insulator
Instead of traveling through inside – travel outside: A B 0 l d E 0 < = = Δ B A A B BA l d E V V V E dipoles, average Potential Difference in an Insulator

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Electric field in capacitor filled with insulator: E net = E plates -E dipoles p = α E plates E dipoles ~E plates E net = E plates -KE plates = E plates ( 1-K ) E net = E plates K E plates = Q / A ( ) ε 0 E net = Q / A ( ) K 0 K – dielectric constant Dielectric Constant
Dielectric constant for various insulators: vacuum 1 (by definition)

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Lecture 11 - Potential at a Certain Location 1 Add up the...

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