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Unformatted text preview: 79 Chapter 22 The Electric Field 2: Continuous Charge Distributions Conceptual Problems *1 ( a ) False. Gausss law states that the net flux through any surface is given by inside S n net 4 kQ dA E = = . While it is true that Gausss law is easiest to apply to symmetric charge distributions, it holds for any surface. ( b ) True 2 Determine the Concept Gausss law states that the net flux through any surface is given by inside S n net 4 kQ dA E = = . To use Gausss law the system must display some symmetry. 3 Determine the Concept The electric field is that due to all the charges, inside and outside the surface. Gausss law states that the net flux through any surface is given by inside S n net 4 kQ dA E = = . The lines of flux through a Gaussian surface begin on charges on one side of the surface and terminate on charges on the other side of the surface. 4 Picture the Problem We can show that the charge inside a sphere of radius r is proportional to r 3 and that the area of a sphere is proportional to r 2 . Using Gausss law, we can show that the field must be proportional to r 3 / r 2 = r . Use Gausss law to express the electric field inside a spherical charge distribution of constant volume charge density: A kQ E inside 4 = where 2 4 r A = . Express Q inside as a function of and r : 3 3 4 inside r V Q = = Substitute to obtain: r k r r k E 3 4 4 4 2 3 3 4 = = Chapter 22 80 *5 ( a ) False. Consider a spherical shell, in which there is no charge, in the vicinity of an infinite sheet of charge. The electric field due to the infinite sheet would be non-zero everywhere on the spherical surface. ( b ) True (assuming there are no charges inside the shell). ( c ) True. ( d ) False. Consider a spherical conducting shell. Such a surface will have equal charges on its inner and outer surfaces but, because their areas differ, so will their charge densities. 6 Determine the Concept Yes. The electric field on a closed surface is related to the net flux through it by Gausss law: inside S = = Q EdA . If the net flux through the closed surface is zero, the net charge inside the surface must be zero by Gausss law. 7 Determine the Concept The negative point charge at the center of the conducting shell induces a charge + Q on the inner surface of the shell. correct. is ) ( a 8 Determine the Concept The negative point charge at the center of the conducting shell induces a charge + Q on the inner surface of the shell. Because a conductor does not have to be neutral, correct. is ) ( d *9 Determine the Concept We can apply Gausss law to determine the electric field for r < R 1 and r > R 2 . We also know that the direction of an electric field at any point is determined by the direction of the electric force acting on a positively charged object located at that point....
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This homework help was uploaded on 02/26/2008 for the course PHYSICS 11 taught by Professor Licini during the Spring '07 term at Lehigh University .
- Spring '07