8B - 3_Gauss_shape_11.ppt

8B - 3_Gauss_shape_11.ppt - Introduction to Gauss Law We...

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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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3 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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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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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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Flux of a vector v through an A rea A flux is θ is the angle between v and the outward normal to A .
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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 “*lux” of *ield 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 True for ALL surfaces Useful (to calculate E) for SOME surfaces and symmetries. Desired E : Constant over the surface (by symmetry). Try to find surface so that E
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8B - 3_Gauss_shape_11.ppt - Introduction to Gauss Law We...

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