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gauss' law 1

# gauss' law 1 - Carl Friedrich Gauss 1777-1855 Last Week...

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1 1 Gauss’ Law – I Carl Friedrich Gauss 1777-1855 This lecture: HRW 23.1-23.5 For next time: HRW 23.6-23.9 2 Last Week Electric Field A vector field that pervades space The electric force on a particle is the field times its charge Electric field lines help visualize electric fields The density of lines is proportional to the magnitude of the field The electric field is tangent to the electric field line How to calculate the electric field from: Collections of point charges Continuous charge distributions Today Electric Flux Gauss’ Law Spherical symmetry Cylindrical symmetry Planar symmetry 3 E d a a E Area = a Electric flux da is a vector normal to each patch in the outward direction , and has a magnitude a . Inward E gives negative Φ Outward E gives positive The total flux is the sum over all the surface elements: Any surface can be broken up into infinitesimal planar patches. The Electric Flux through a patch is given by r r dd Φ = E • a == ∫∫ r r ΦΦ Ea surface integral 4 θ E Area = A normal Electric Flux through a Planar Surface For the special case of a planar surface of area, A, and a uniform field, E, that makes an angle with respect to normal: ˆˆ ˆ . •= r r r Φ =EnA En A =E nA = EAcos θ Qualitatively, flux is the number of field lines crossing an area A. Units of flux: N m 2 /C Why the dot product? It’s like the “flow of water” through a surface. Eg., the flux through all these surfaces is the same.

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gauss' law 1 - Carl Friedrich Gauss 1777-1855 Last Week...

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