Chapter 22 Electric Fields

1. Chapter 22 Electric Fields In this chapter we will introduce the concept of an electric field. As long as charges are stationary, Coulomb’s law describes adequately the forces among charges. If the charges are not stationary we must use an alternative approach by introducing the electric field (symbol ). In connection with the electric field, the following topics will be covered: -Calculating the electric field generated by a point charge. -Using the principle of superposition to determine the electric field created by a collection of point charges as well as continuous charge distributions. -Once the electric field at a point P is known, calculating the electric force on any charge placed at P. -Defining the notion of an “electric dipole.” Determining the net force, the net torque, exerted on an electric dipole by a uniform electric field, as well as the dipole potential energy. (22-1)

2. In Chapter 21 we discussed Coulomb’s law, which gives the force between two point charges. The law is written in such a way as to imply that q2 acts on q1at a distance rinstantaneously (“action at a distance”): Electric interactions propagate in empty space with a large butfinite speed (c = 3108 m/s). In order to take into account correctly the finite speed at which these interactions propagate, we have to abandon the “action at a distance” point of view and still be able to explain how q1 knows about the presence of q2 . The solution is to introduce the new concept of anelectric fieldvectoras follows: Point charge q1 does not exert a force directly on q2. Instead, q1 creates in its vicinity an electric field that exerts a force on q2 . (22-2)

3. (22-3)

4. P qo r q (22-4)

5. O O (22-5)

6. Checkpoint 1: • The figure here shows a proton p and an electron e on an x-axis. What is the direction of the electric field due to the electron at • Point S and • Point R ? • What is the direction of the net electric filed at • c) Point R and • d) Point S?

11. Example 1:

12. Example 2:

13. +q/2 +q/2 + q d - q -q (22-6)

14. (22-7)

15. dE P r dV dq (22-8)

16. C A dq (22-9)

17. electric field line P Q P electric field lines (22-10)

18. (22-11)

19. q q (22-12)

20. (22-13)

21. F+ F- x-axis (22-14)

22. B U  180˚ A (22-15)

23. Fig. a Fig. b (22-16)

24. Checkpoint 4: • The figure shows four orientations of an electric dipole in an external electric field. Rank the orientations according to : • The magnitude of the torque on the dipole • The potential energy of the dipole • Greatest first.

29. Checkpoint 3: • In the figure, what is the direction of the electrostatic force on the electron due to the external electric filed shown? • In which direction will the electron accelerate if its moving parallel to the y axis before it encounters the external filed? • If, instead, the electron is initially moving rightward, will its speed increase, decrease, or remain constant?

30. Example 3:

31. Example 4:

32. Example 5:

33. Example 6:

34. Example 7:

35. Example 8:

36. Example 9:

37. Example 10:

38. Example 11:

39. Example 12:

40. Example 13:

41. Example 14:

42. Example 15:

43. Example 16:

44. Example 17: