8B 4_Gauss - Introduction to Gauss Law We earlier said that the strength of the electric field was proportional to the density of field lines Now

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Introduction to Gauss’ Law We earlier said that the strength of the electric field was proportional to the density of field lines. Now we show that the total number of field lines (“flux”) passing through a closed surface is proportional to the charge within the surface. This is “Gauss’ Law”
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Electric Flux  Number of lines Means related to, or proportional to E (Number of Lines) / Area = Flux / Area Flux E × Area
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Vector E and Area A flux is θ is the angle between v and the outward normal to A .
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Area Element d A : Closed Surface Definition of direction of A : For closed surface, d A is normal to surface and points outward (from inside to outside). Φ E > 0 if E points out. Φ E < 0 if E points in.
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5 Open and Closed Surfaces A rectangle is an open surface — it does NOT contain a volume. A sphere is a closed surface — it DOES contain a volume.
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Case II: E is constant vector field directed at angle θ to planar surface S of area A Electric Flux Φ E E d ! = " ## E A r r ˆ d dA = A n r ˆ n
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Electric Flux Electric flux, Φ E × Area Total flux through a closed surface: (The “dot” product means |E| | Δ A| cos θ ) For infinitesimal areas
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8 Gauss’s Law – The Idea The total “flux” of field lines penetrating any of these surfaces is the same and depends only on the amount of charge inside.
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Choosing Gaussian Surfaces Desired E : Constant over the surface (by symmetry). Try to find surface so that E
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This note was uploaded on 02/08/2009 for the course PHYSICS 8B taught by Professor Shapiro during the Spring '07 term at University of California, Berkeley.

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8B 4_Gauss - Introduction to Gauss Law We earlier said that the strength of the electric field was proportional to the density of field lines Now

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