PPE09_UsingGausssLaw1 - Electric Fields Electric Fields...

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Unformatted text preview: Electric Fields Electric Fields Using Gausss Law Using Gausss Law RHJansen Spherical Gaussian Surfaces RHJansen Gaussian Surfaces are drawn to match the geometry of the enclosed charge distribution. Point charges are spheres. Spherical charges are obviously spheres. The Gaussian Surface drawn around a spherical charge must be a sphere as well. Explanation to follow. Example 1 P RHJansen Finding the electric field at a point P near a proton a. Draw a symmetrical Gaussian Surface around the charge distribution. Remember it looks like a circle in this 2D drawing, but it is actually a sphere. Always think 3D. It must mimic the shape of the charge distribution. A point charge is a sphere, so the Gaussian Surface is a sphere. It must be centered on the charge distribution. It must pass through the point you want to analyze, point P . b. Why is the surface drawn this way? This is done so that the entire electric field passes through the surface, and so that the strength of the electric field is the same at every point on the surface. This make E a constant value that does not require integration. Example 1 P RHJansen Finding the electric field at a point P near a proton c. Write the original version of Gausss Law. d. E is constant on the surface and can be moved outside the integral. 3. Integrate the area, unless of course you already know the area of a sphere. f. Rearrange and solve. E E E = E dA = E 4 2 ( 29 = E = 4 2 E = 1 4 2 E = 2 Conductors and Insulators There are two types of objects that can hold excess charge: Conductors Insulators First we will examine how excess charges are distributed in each case. Then we will use the Gaussian surface to calculate and graph the electric field in and around spherical conductors and insulators. RHJansen Excess Charge Distribution in Conductors + + + + + + + + + + + + + + + + Positive charges follow the field Negative charges move opposite the field Excess charge piles up on a conductors surface. RHJansen In conductors charges are free to move. Extra charges on a conductor repel each other, along electric field lines. Excess Charge Distribution in Conductors Once the charges are on the surface the interior become neutral. There is no electric field inside a conductor. + + + + + + + + + + + + + + + + RHJansen Important ! You do not have to be told about the charge distribution on a conductor. If the conductor has an excess charge the charges pile up on the surface of the conductor....
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This note was uploaded on 07/21/2009 for the course PHYSICS 7B taught by Professor Packard during the Spring '08 term at University of California, Berkeley.

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PPE09_UsingGausssLaw1 - Electric Fields Electric Fields...

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