Electric charge

1. Electric charge • Glass rods, plastic tubes, silk, and fur can be used to demonstrate the movement of electrons and how their presence or absence make for powerful forces of attraction and repulsion.

2. Q21.1 When you rub a plastic rod with fur, the plastic rod becomes negatively charged and the fur becomes positively charged. As a consequence of rubbing the rod with the fur, A. the rod and fur both gain mass. B. the rod and fur both lose mass. C. the rod gains mass and the fur loses mass. D. the rod loses mass and the fur gains mass. E. none of the above

3. A21.1 When you rub a plastic rod with fur, the plastic rod becomes negatively charged and the fur becomes positively charged. As a consequence of rubbing the rod with the fur, A. the rod and fur both gain mass. B. the rod and fur both lose mass. C. the rod gains mass and the fur loses mass. D. the rod loses mass and the fur gains mass. E. none of the above

4. Q21.2 A positively-charged piece of plastic exerts an attractive force on an electrically neutral piece of paper. This is because A. electrons are less massive than atomic nuclei. B. the electric force between charged particles decreases with increasing distance. C. an atomic nucleus occupies only a small part of the volume of an atom. D. a typical atom has many electrons but only one nucleus.

5. A21.2 A positively-charged piece of plastic exerts an attractive force on an electrically neutral piece of paper. This is because A. electrons are less massive than atomic nuclei. B. the electric force between charged particles decreases with increasing distance. C. an atomic nucleus occupies only a small part of the volume of an atom. D. a typical atom has many electrons but only one nucleus.

6. Q21.3 Three point charges lie at the vertices of an equilateral triangle as shown. All three charges have the same magnitude, but Charges #1 and #2 are positive (+q) and Charge #3 is negative (–q). The net electric force that Charges #2 and #3 exert on Charge #1 is in Charge #2 +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

7. A21.3 Charge #2 Three point charges lie at the vertices of an equilateral triangle as shown. All three charges have the same magnitude, but Charges #1 and #2 are positive (+q) and Charge #3 is negative (–q). The net electric force that Charges #2 and #3 exert on Charge #1 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

8. Charles Coulomb determined the electrostatic force law • Coulomb’s Law allows the calculation of electrostatic attraction or repulsion.

9. Q21.4 Charge #2 Three point charges lie at the vertices of an equilateral triangle as shown. All three charges have the same magnitude, but Charge #1 is positive (+q) and Charges #2 and #3 are negative (–q). The net electric force that Charges #2 and #3 exert on Charge #1 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. A21.4 Charge #2 Three point charges lie at the vertices of an equilateral triangle as shown. All three charges have the same magnitude, but Charge #1 is positive (+q) and Charges #2 and #3 are negative (–q). The net electric force that Charges #2 and #3 exert on Charge #1 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

11. Examples of electrical force calculated—I • A fascinating comparison of gravitational force to electrostatic force is shown in Example 21.1 and Figure 21.11. • Regard Problem-Solving Strategy 21.1. • See also Example 21.2 and Figure 21.12.

12. Examples of electrical force calculated—II • Consider Example 21.3 and Figure 21.13. • See also Example 21.4 and Figure 21.14.

13. Q21.5 A positive point charge +Q is released from rest in an electric field. At any later time, the velocity of the point charge A. is in the direction of the electric field at the position of the point charge. B. is directly opposite the direction of the electric field at the position of the point charge. C. is perpendicular to the direction of the electric field at the position of the point charge. D. is zero. E. not enough information given to decide

14. A21.5 A positive point charge +Q is released from rest in an electric field. At any later time, the velocity of the point charge A. is in the direction of the electric field at the position of the point charge. B. is directly opposite the direction of the electric field at the position of the point charge. C. is perpendicular to the direction of the electric field at the position of the point charge. D. is zero. E. not enough information given to decide

15. Electric fields may be mapped by force on a test charge • If one measured the force on a test charge at all points relative to another charge or charges, an electric field may be mapped. • This experiment is often done in one’s mind (called a “gedanken experiment”).

16. Electric fields I—the point charge • Fields of force may be sketched for different arrangements of charge. • Consider Example 21.6 and Figure 21.19.

17. Electric fields II—charges in motion within a field • Consider Example 21.7. • Consider Example 21.8 and Figure 21.21.

18. Q21.6 Charge #1 Two point charges and a point P lie at the vertices of an equilateral triangle as shown. Both point charges have the same magnitude q but opposite signs. There is nothing at point P. The net electric field that Charges #1 and #2 produce at point P is in –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

19. A21.6 Charge #1 Two point charges and a point P lie at the vertices of an equilateral triangle as shown. Both point charges have the same magnitude q but opposite signs. There is nothing at point P. The net electric field that Charges #1 and #2 produce at point P is in –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

21. Consider force and torque on a dipole • Regard Figure 21.32. • Follow Example 21.14 and Figure 21.33.

22. Q21.7 Charge #1 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 –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

23. A21.7 Charge #1 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 –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

24. Q21.8 The illustration shows the electric field lines due to three point charges. The electric field is strongest A. where the field lines are closest together. B. where the field lines are farthest apart. C. where adjacent field lines are parallel. D. none of the above

25. A21.8 The illustration shows the electric field lines due to three point charges. The electric field is strongest A. where the field lines are closest together. B. where the field lines are farthest apart. C. where adjacent field lines are parallel. D. none of the above

26. Electric field lines map out regions of equivalent force I

27. 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

28. 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

29. Electric fields add as vectors • Regard Figure 21.22. • Review Problem-Solving Strategy 21.2. • Follow Example 21.9 and Figure 21.23.

30. A field around a ring or line of charge • Review Example 21.10 and Figure 21.24. • Review Example 21.11 and Figure 21.25.

31. A field around a disk or sheet of charge • Review Example 21.12 and Figure 21.26. • Review Example 21.13 and Figure 21.27.

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

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

34. Q21.11 Charge #2 +q 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 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

35. A21.11 Charge #2 +q 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 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