Chapter 21

1. Chapter 21 Electric Fields and Dipoles (cont.)

2. Q21.7 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 Charge #1 –q P y –q x Charge #2 A. the +x-direction. B. the –x-direction. C. the +y-direction. D. the –y-direction. E. none of the above

3. A21.7 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 Charge #1 –q P y –q x Charge #2 A. the +x-direction. B. the –x-direction. C. the +y-direction. D. the –y-direction. E. none of the above

4. Q21.9 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

5. 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. Q21.10 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 #2 +q Charge #1 +q y –q A. clockwise. B. counterclockwise. C. zero. D. not enough information given to decide x Charge #3

7. A21.10 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 #2 +q Charge #1 +q y –q A. clockwise. B. counterclockwise. C. zero. D. not enough information given to decide x Charge #3

8. Q21.11 Charge #2 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 +q Charge #1 +q y –q x Charge #3 A. the +x-direction. B. the –x-direction. C. the +y-direction. D. the –y-direction. E. none of the above

9. A21.11 Charge #2 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 +q Charge #1 +q y –q x Charge #3 A. the +x-direction. B. the –x-direction. C. the +y-direction. D. the –y-direction. E. none of the above

10. Chapter 22 Gauss’s Law

11. Gauss’s law is an alternative to Coulomb’s law and is completely equivalent to it. • Carl Friedrich Gauss, shown below, formulated this law. Gauss’s Law

12. 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.) Charge and electric flux

13. 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. Zero net charge inside a box

14. 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. What affects the flux through a box?

15. Electric Flux Through a Rectangular Surface Calculating electric flux

16. Electric flux through a disk

17. Evaluate total Electric Flux through cube. Electric flux through a cube

18. Calculate total Flux due to point charge. Electric flux through a sphere

19. 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. Point charge centered in a spherical surface

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

21. Figure 22.14 below shows that flux is positive if the enclosed charge is positive, and negative if the charge is negative. Positive and negative flux

22. Q22.1 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 +q greater. the same. C. less, but not zero. D. zero. E. not enough information given to decide Gaussian surface #1 Gaussian surface #2

23. A22.1 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 +q greater. the same. C. less, but not zero. D. zero. E. not enough information given to decide Gaussian surface #1 Gaussian surface #2

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

25. Q22.2 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? Only surface A Only surface B C. Only surface C D. Only surface D E. Both surface C and surface D

26. A22.2 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? Only surface A Only surface B C. Only surface C D. Only surface D E. Both surface C and surface D