PHY108 - Chapter 23

PHY108 - Chapter 23 - Chapter 23: Gauss Law Questions to...

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Chapter 23: Gauss’ Law Questions to Answer oWhat is f lux? 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 23 we learned that there is an electrostatic force between charges. The magnitude and direction of the force are given by Coulomb’s Law Ch. 24: Gauss’ Law 12 2 12 e 12 qq Fk r r = JJG ± •We then learned 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 ei 2 i i q Ek r r = JG e Fq E m a == J GJ G G
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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. 24: Gauss’s Law
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How can you catch the most fish?
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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 JG B xx yy zz AB A B A B A B ABcos θ ⋅= + + = J GJ G ± xyz BB iB j B k =++ ±± ± AA i A j A k Note: BA ⋅=⋅ JG JG A B When θ = 90º 0 =
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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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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.
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PHY108 - Chapter 23 - Chapter 23: Gauss Law Questions to...

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