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Unformatted text preview: Chapter 23 Gauss Law The new concept: flux of the electric field ( symbol ) Introduce the Gauss law and apply it to determine the electric filed generated by A point charge An infinite, uniformly charged insulating plane 1 An infinite, uniformly charged insulating rod A uniformly charged spherical shell A uniform spherical charge distribution Apply Gauss law to determine the electric field inside and outside charged conductors Introduce area vector A which has the magnitude equal to A and the direction of the loop normal. Then Note: Flux depends on A v vA r r = = cos Flux n Consider an airstream of velocity v which is aimed at a loop of area A . The velocity vector v is at angle with respect to the loop normal . The product vA cos is known as the flux . (In this example the flux is equal to the volume flow rate through the loop) n 2 n It is maximal and equals to vA when = It is minimal and equals to when = 90 Consider the closed surface shown in the figure. Assume we know the electric field E in the vicinity of the surface. We define flux of the electric field through the surface as follows: Divide the surface into small elements of area A or each element calculate the flux Flux of an Electric Field 3 For each element calculate the flux  Then calculate the sum  Let element A be infinitely small so that the sum becomes an integral A E A E cos = r r = A E r r = A d E r r SI units: Nm 2 /C Electric field flux through a closed surface is given by The loop on the integral indicates that integration surface is closed. Such closed surface is called = A d E r r Flux of an Electric Field (contd) 4 Gaussian surface Since magnitude of the electric field is proportional to the density of the field lines, we can conclude that: The electric field flux through a Gaussian surface is proportional to the net number of electric field lines passing through that surface Gauss law relates the net flux of an electric field through a closed surface (a Gaussian surface) to the net charge q enc that is enclosed by that surface In equation form: ausss law holds for ny losed surface. In practice a particular enc q A d E = r r or equivalently enc q = Gauss Law 5 n n n Gausss law holds for any closed surface. In practice a particular surface makes the problem of determining the field very simple When calculating the net charge inside a closed surface we take into account the algebraic signs of all charges enclosed If enclosed charge q enc is positive, the net electric flux is outward; if enclosed charge q enc is negative, then the net flux is inward When applying Gauss law for a closed surface we ignore the charges outside the surface (no matter how large they are) Example : Calculate the net flux through...
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 Fall '08
 IASHVILI
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