1. Copyright © 2012 Pearson Education Inc. PowerPoint ® Lectures for University Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Chapter 22 Gauss’s Law

2. Copyright © 2012 Pearson Education Inc. Goals for Chapter 22 To use the electric field at a surface to determine the charge within the surface To learn the meaning of electric flux and how to calculate it To learn the relationship between the electric flux through a surface and the charge within the surface To use Gauss’s law to calculate electric fields To learn where the charge on a conductor is located

3. Copyright © 2012 Pearson Education Inc. Charge and electric flux Positive charge within the box produces outward electric flux through the surface of the box, and negative charge produces inward flux.

4. Copyright © 2012 Pearson Education Inc. Zero net charge inside a box Zero net charge inside a box and no net electric flux through the surface of the box.

5. Copyright © 2012 Pearson Education Inc. What affects the flux through a box? Doubling the charge within the box doubles the flux, but doubling the size of the box does not change the flux.

6. Copyright © 2012 Pearson Education Inc. Calculating electric flux For uniform electric field For nonuniform electric field

7. Copyright © 2012 Pearson Education Inc. Electric flux through a disk

8. Copyright © 2012 Pearson Education Inc. Electric flux through a cube

9. Copyright © 2012 Pearson Education Inc. Electric flux through a sphere Ex 22.3: Find the electric flux through the sphere. q = 3 μC, r = 0.2 m. Note: the electric flux is independent of the sphere size Gauss’s Law

10. Copyright © 2012 Pearson Education Inc. Point charge centered in a spherical surface The flux through the sphere is independent of the size of the sphere and depends only on the charge inside.

11. Copyright © 2012 Pearson Education Inc. Point charge inside a nonspherical surface The flux is independent of the surface and depends only on the charge inside.

12. Copyright © 2012 Pearson Education Inc. Positive and negative flux The flux is positive if the enclosed charge is positive, and negative if the charge is negative.

13. Copyright © 2012 Pearson Education Inc. General form of Gauss’s law What is the electric flux at service areas A, B, C, D?

14. Copyright © 2012 Pearson Education Inc. Applications of Gauss’s law Under electrostatic conditions, any excess charge on a conductor resides entirely on its surface. Example 22.5: Find the electric field of charged sphere at distance r.

15. Copyright © 2012 Pearson Education Inc. Field of a line charge Example 22.6: Find the electric field of an infinite long uniform line charge.

16. Copyright © 2012 Pearson Education Inc. Field of a sheet of charge Example 22.7: Find the electric field of an infinite plane sheet of charge.

17. Copyright © 2012 Pearson Education Inc. Field between two parallel conducting plates Example 22.8: Find the electric field between oppositely charged parallel conducting plates.

18. Copyright © 2012 Pearson Education Inc. A uniformly charged sphere Example 22.9: Find the electric field both inside and outside a sphere uniformly filled with charge. Follow Example 22.10 for the charge on a hollow sphere.

19. Copyright © 2012 Pearson Education Inc. Charges on conductors Charges in a conductor having a cavity within it.

20. Copyright © 2012 Pearson Education Inc. A conductor with a cavity A solid conductor with a cavity carries a total charge of +7 nC. Within the cavity, insulated from the conductor, is a point charge of -5 nC. How much charge is on each surface (inner and outer) of the conductor?

21. Copyright © 2012 Pearson Education Inc. Testing Gauss’s law experimentally Follow the discussion of Faraday’s icepail experiment, which confirmed the validity of Gauss’s law. Use Figure 22.25 below.

22. Copyright © 2012 Pearson Education Inc. The Van de Graaff generator The Van de Graaff generator, shown in Figure 22.26 below, operates on the same principle as in Faraday’s icepail experiment.

23. Copyright © 2012 Pearson Education Inc. Electrostatic shielding A conducting box (a Faraday cage) in an electric field shields the interior from the field. (See Figure 22.27 below.)

24. Copyright © 2012 Pearson Education Inc. Field at the surface of a conductor The electric field at the surface of any conductor is always perpendicular to the surface and has magnitude  /  0. Follow the discussion in the text, using Figure 22.28 at the right. Follow Conceptual Example 22.12. Follow Example 22.13, which deals with the electric field of the earth.