Ch23Sp09AGM - C hapte 23 Gauss Law r Que stions to Answe r...

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Chapter 23: Gauss’ Law Questions to Answer o What is flux? o What is Gauss’ Law? o How is Gauss’ Law useful? o What is the electric field in an isolated conductor? o Where does charge go for an isolated conductor? o How do you calculate the net force on a charge due to a countinuous distribution of charge?
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In Chapter 21 we learned that there is an electrostatic force between charges. The magnitude and direction of the force are given by Coulomb’s Law Ch. 23: Gauss’ Law 1 2 2 12 e 12 q q F k r r = uur $ We then learned in Chapter 22 that we can characterize a system of charges by the electric field they produce. If we calculate the electric field for a point P is space produced by a system of charges, we then know the net force on any charged particle q placed at P: $ i e i 2 i i q E k r r = ur e F qE ma = = ur ur r
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In this chapter we learn Gauss’s Law. This fundamental law is one of Maxwell’s equations, which define all electromagnetism. In addition Gauss’s Law allows us to exploit symmetry in many situations to easily determine the electric field of a system Through Gauss’s Law we can also determine some fundamental electrical properties of conductors Ch. 23: Gauss’s Law
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How can you catch the most fish?
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What is FLUX? First consider a fluid example: the rate that water flows through a pipe = the flux Air Flow Demo: total flow of air THROUGH the panel, THE FLUX, is dependent on the orientation of panel relative to the direction of air flow. When the direction of flow is perpendicular to the surface we had the maximum FLUX. When the direction of flow was parallel to the surface we had NO FLUX! How can we quantitatively describe this phenomenon?
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To get going on Gauss’s Law we first have to understand the idea of FLUX First a review of some vector calculus: θ A ur B ur x x y y z z A B A B A B A B ABcos θ = + + = ur ur $ x y z B B i B j B k = + + ur $ $ $ x y z A A i A j A k = + + ur $ $ Note: A B B A = ur ur ur ur A ur B ur When θ = 90º A B 0 = ur ur
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When we discuss surfaces, we associate a vector with every point on that surface, the surface normal: Now let’s look at our demo result again, but with the surface vectors and the flow vectors drawn in. When
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This note was uploaded on 03/26/2010 for the course PHY 108 taught by Professor Iashvili during the Spring '08 term at SUNY Buffalo.

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Ch23Sp09AGM - C hapte 23 Gauss Law r Que stions to Answe r...

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