CHAPTER 22 GAUSS’S LAW TWO BASIC CONCEPTS ELECTRIC FLUX AND GAUSS’S LAW 1 ELECTRIC FLUX Consider a number of guns at the left shooting to the right. Bullets Sheet Flux of bullets is number of bullets times area of sheet perpendicular to bullets. 2 Turn sheet on edge. Bullets Sheet Flux now near zero since area of sheet is parallel to bullets. 3 Turn sheet to angle. Bullets Sheet Flux somewhere between previous two values. 4 Assign area vector to sheet. Bullets φ Sheet A Flux will be 5 OR THINK ABOUT FLUX THE WAY YOUR BOOK DOES. 6 7 FOR ELECTRIC FLUX ELECTRIC FIELD φ Sheet A 8 WHAT WE HAVE DISCUSSED IS FOR A UNIFORM ELECTRIC FIELD. If the field varies we must use differential calculus. Small increment of flux d Then integrate 9 GAUSS’S LAW We will state the law then work some examples. After that we will do an example to justify the law. Statement of Gauss’s law: The flux through a closed surface is equal to the net charge enclosed by the surface divided by ε0. Equation: 10 Consider a conducting sphere of radius R with charge q on the surface. 11 Draw a Gaussian surface around this sphere with radius r. Apply Gauss’s Law 12 The same equation we had for a point charge. 13 Example 22.9 Positive electric charge Q is distributed uniformly throughout the volume of an insulating sphere with radius R. a. Find the electric field at point p where r < R. b. Find the electric field at point p where r > R. 14 15 a. Radius of Gaussian Surface = r Gauss’s Law Need charge enclosed by surface. Charge density Charge enclosed by Gaussian Surface 16 17 For r < R 18 Part b. Draw Gaussian Surface outside sphere. 19 Integral same as before 20 JUSTIFY GAUSS’S LAW Gauss’s Law Coulomb’s Law Consider point charge Q Q r At P P E Visualize a sphere centered on Q and with radius r passing through P. 21 Integrate over surface. 22 Other Geometries Line of charge Charge on wire? Charge per unit length λ Choose Gaussian surface – cylinder 23 Cylinder made up of two ends and cylindrical surface. ·
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26 Infinite sheet of charge. Remember in Chapter 21 we got 2
where σ was the charge per unit area. Choose cylinder for Gaussian surface. 27 Cylinder made up of two ends and cylindrical surface. 28 ·
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Cylinder made up of two ends and cylindrical surface. 0
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Charge enclosed 30 0
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