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Download Summary 738 Chapter 24 Gauss's Law
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738 Chapter 24 Gauss’s Law Chapter 24 Gauss's Law Summary Definition Electric flux is proportional to the number of electric field lines that penetrate a surface. If the electric field is uniform and makes an angle u with the normal to a surface of area A, the electric flux through the surface is In general, the electric flux through a surface is FE 5 EA cos u (24.2) FE ; 3 E ? d A (24.3) S S surface Concepts and Principles Gauss’s law says that the net electric flux FE through any closed gaussian surface is equal to the net charge q in inside the surface divided by P0: q in S S FE 5 C E ? d A 5 P0 (24.6) Using Gauss’s law, you can calculate the electric field due to various symmetric charge distributions. Objective Questions A conductor in electrostatic equilibrium has the following properties: 1. The electric field is zero everywhere inside the conductor, whether the conductor is solid or hollow. 2. If the conductor is isolated and carries a charge, the charge resides on its surface. 3. The electric field at a point just outside a charged conductor is perpendicular to the surface of the conductor and has a magnitude s/P0, where s is the surface charge density at that point. 4. On an irregularly shaped conductor, the surface charge density is greatest at locations where the radius of curvature of the surface is smallest. 1. denotes answer available in Student Solutions Manual/Study Guide 1. A cubical gaussian surface surrounds a long, straight, charged filament that passes perpendicularly through two opposite faces. No other charges are nearby. (i) Over how many of the cube’s faces is the electric field zero? (a) 0 (b) 2 (c) 4 (d) 6 (ii) Through how many of the cube’s faces is the electric flux zero? Choose from the same possibilities as in part (i). 2. A coaxial cable consists of a long, straight filament surrounded by a long, coaxial, cylindrical conducting shell. Assume charge Q is on the filament, zero net charge is on the shell, and the electric field is E1 ^i at a particular point P midway between the filament and the inner surface of the shell. Next, you place the cable into a uniform external field 2E ^i. What is the x component of the electric field at P then? (a) 0 (b) between 0 and E 1 (c) E 1 (d) between 0 and 2E 1 (e) 2E 1 3. In which of the following contexts can Gauss’s law not be readily applied to find the electric field? (a) near a long, uniformly charged wire (b) above a large, uniformly charged plane (c) inside a uniformly charged ball (d) outside a uniformly charged sphere (e) Gauss’s law can be readily applied to find the electric field in all these contexts. 4. A particle with charge q is located inside a cubical gaussian surface. No other charges are nearby. (i) If the particle is at the center of the cube, what is the flux through each one of the faces of the cube? (a) 0 (b) q/2P0 (c) q/6P0 (d) q/8P0 (e) depends on the size of the cube (ii) If the particle can be moved to any point within the cube, what maximum value can the flux through one face approach? Choose from the same possibilities as in part (i). 5. Charges of 3.00 nC, 22.00 nC, 27.00 nC, and 1.00 nC are contained inside a rectangular box with length 1.00 m, width 2.00 m, and height 2.50 m. Outside the box are charges of 1.00 nC and 4.00 nC. What is the electric flux through the surface of the box? (a) 0 (b) 25.64 3 102 N ? m2/C (c) 21.47 3 103 N ? m2/C (d) 1.47 3 103 N ? m2/C (e) 5.64 3 102 N ? m2/C 6. A large, metallic, spherical shell has no net charge. It is supported on an insulating stand and has a small hole at the top. A small tack with charge Q is lowered on a silk thread through the hole into the interior of the shell. (i) What is the charge on the inner surface of the shell, (a) Q (b) Q /2 (c) 0 (d) 2Q /2 or (e) 2Q? Choose your answers to the following questions from