1. © 2012 Pearson Education, Inc. { Chapter 21 Electric Fields and Dipoles (cont.)

2. © 2012 Pearson Education, Inc. Two point charges and a point P lie at the vertices of an equilateral triangle as shown. Both point charges have the same negative charge (–q). There is nothing at point P. The net electric field that charges #1 and #2 produce at point P is in Q21.7 Charge #1 Charge #2 –q–q –q–q x y P A. the +x-direction.B. the –x-direction. C. the +y-direction. D. the –y-direction. E. none of the above

3. © 2012 Pearson Education, Inc. Two point charges and a point P lie at the vertices of an equilateral triangle as shown. Both point charges have the same negative charge (–q). There is nothing at point P. The net electric field that charges #1 and #2 produce at point P is in A21.7 A. the +x-direction.B. the –x-direction. C. the +y-direction. D. the –y-direction. E. none of the above Charge #1 Charge #2 –q–q –q–q x y P

4. © 2012 Pearson Education, Inc. Q21.9 A. the +x-direction. B. the –x-direction. C. the +y-direction. D. the –y-direction. E. none of the above Positive charge is uniformly distributed around a semicircle. The electric field that this charge produces at the center of curvature P is in

5. © 2012 Pearson Education, Inc. A21.9 Positive charge is uniformly distributed around a semicircle. The electric field that this charge produces at the center of curvature P is in A. the +x-direction. B. the –x-direction. C. the +y-direction. D. the –y-direction. E. none of the above

6. © 2012 Pearson Education, Inc. Q21.10 Charge #1 Charge #2 Charge #3 +q+q +q+q –q–q x y A. clockwise. B. counterclockwise. C. zero. D. not enough information given to decide Three point charges lie at the vertices of an equilateral triangle as shown. Charges #2 and #3 make up an electric dipole. The net electric torque that charge #1 exerts on the dipole is

7. © 2012 Pearson Education, Inc. A21.10 A. clockwise. B. counterclockwise. C. zero. D. not enough information given to decide Three point charges lie at the vertices of an equilateral triangle as shown. Charges #2 and #3 make up an electric dipole. The net electric torque that charge #1 exerts on the dipole is Charge #1 Charge #2 Charge #3 +q+q +q+q –q–q x y

8. © 2012 Pearson Education, Inc. Q21.11 Charge #1 Charge #2 Charge #3 +q+q +q+q –q–q x y A. the +x-direction.B. the –x-direction. C. the +y-direction. D. the –y-direction. E. none of the above Three point charges lie at the vertices of an equilateral triangle as shown. Charges #2 and #3 make up an electric dipole. The net electric force that charge #1 exerts on the dipole is in

9. © 2012 Pearson Education, Inc. A21.11 Three point charges lie at the vertices of an equilateral triangle as shown. Charges #2 and #3 make up an electric dipole. The net electric force that charge #1 exerts on the dipole is in A. the +x-direction.B. the –x-direction. C. the +y-direction. D. the –y-direction. E. none of the above Charge #1 Charge #2 Charge #3 +q+q +q+q –q–q x y

10. © 2012 Pearson Education, Inc. { Chapter 22 Gauss’s Law

11. © 2012 Pearson Education, Inc. Gauss’s Law Gauss’s law is an alternative to Coulomb’s law and is completely equivalent to it. Gauss’s law is an alternative to Coulomb’s law and is completely equivalent to it. Carl Friedrich Gauss, shown below, formulated this law. Carl Friedrich Gauss, shown below, formulated this law.

12. © 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. (See Figure 22.2 below.)

13. © 2012 Pearson Education, Inc. Zero net charge inside a box  Figure below shows three cases in which there is zero net charge inside a box and no net electric flux through the surface of the box.

14. © 2012 Pearson Education, Inc. What affects the flux through a box?  As Figure below shows, doubling the charge within the box doubles the flux, but doubling the size of the box does not change the flux.

15. © 2012 Pearson Education, Inc. Calculating electric flux  Electric Flux Through a Rectangular Surface

16. © 2012 Pearson Education, Inc. Electric flux through a disk

17. © 2012 Pearson Education, Inc. Electric flux through a cube Evaluate total Electric Flux through cube. Evaluate total Electric Flux through cube.

18. © 2012 Pearson Education, Inc. Electric flux through a sphere Calculate total Flux due to point charge. Calculate total Flux due to point charge.

19. © 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. Figure at the right illustrates this fact. The flux through the sphere is independent of the size of the sphere and depends only on the charge inside. Figure at the right illustrates this fact.

20. © 2012 Pearson Education, Inc. Point charge inside a nonspherical surface As before, the flux is independent of the surface and depends only on the charge inside. (See Figure 22.12 below.) As before, the flux is independent of the surface and depends only on the charge inside. (See Figure 22.12 below.)

21. © 2012 Pearson Education, Inc. Positive and negative flux Figure 22.14 below shows that flux is positive if the enclosed charge is positive, and negative if the charge is negative. Figure 22.14 below shows that flux is positive if the enclosed charge is positive, and negative if the charge is negative.

22. © 2012 Pearson Education, Inc. A spherical Gaussian surface (#1) encloses and is centered on a point charge +q. A second spherical Gaussian surface (#2) of the same size also encloses the charge but is not centered on it. Compared to the electric flux through surface #1, the flux through surface #2 is A.greater. B.the same. C. less, but not zero. D. zero. E. not enough information given to decide Q22.1 +q+q Gaussian surface #1 Gaussian surface #2

23. © 2012 Pearson Education, Inc. A spherical Gaussian surface (#1) encloses and is centered on a point charge +q. A second spherical Gaussian surface (#2) of the same size also encloses the charge but is not centered on it. Compared to the electric flux through surface #1, the flux through surface #2 is A.greater. B.the same. C. less, but not zero. D. zero. E. not enough information given to decide A22.1 +q+q Gaussian surface #1 Gaussian surface #2

24. © 2012 Pearson Education, Inc. Using Gauss’s law What is the total Flux through the surfaces A,B,C, and D shown below? iClickers… What is the total Flux through the surfaces A,B,C, and D shown below? iClickers…

25. © 2012 Pearson Education, Inc. Two point charges, +q (in red) and –q (in blue), are arranged as shown. Through which closed surface(s) is the net electric flux equal to zero? Q22.2 A.Only surface A B.Only surface B C. Only surface C D. Only surface D E. Both surface C and surface D

26. © 2012 Pearson Education, Inc. Two point charges, +q (in red) and –q (in blue), are arranged as shown. Through which closed surface(s) is the net electric flux equal to zero? A22.2 A.Only surface A B.Only surface B C. Only surface C D. Only surface D E. Both surface C and surface D