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 A 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 A B E dl Finding Potential Difference
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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 net = E plates K E plates = Q / A ( ) ε 0 E net = Q / A ( ) K ε 0 K – dielectric constant Dielectric Constant
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= Δ B A l d E V s K E Es V plates = = Δ s E plates = Q / A ( ) ε 0 Δ V = Es = Q / A ( ) K ε 0 s K V V vacuum insulator Δ = Δ Potential Difference in a Capacitor with Insulator
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Energy can be stored in electric fields E one _ plate = Q / A ( ) 2 ε 0 (for small s ) U el = Δ 2 0 2 1 ε E volume Δ U el Δ volume ( ) = 1 2 ε 0 E 2 Field energy density: (J/m 3 ) Energy expended by us was converted into energy stored in the electric field
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