In the name of God

1. In the name of God Chapter 5 and 6 by SeyedehSedighehHashemi

2. outline • Electrostatics Is Gauss’ Law • Equilibrium In Electrostatic Field • Equilibrium With Conductors • Stability Of Atoms • The Field Of A Line Charge • A Sheet Of Charge;2 Sheets • A Sphere Of Charge ;A Spherical Shell

4. Carl Friedrich Gauss(30 April 1777 – 23 February 1855)

5. Would a positive charge remain there?

6. There is NO points of stable equilibrium in any electrostatic field. Except right on top of another charge!

7. If were a position of stable equilibrium for a positive charge , the electric field everywhere in the neighborhood would point toward .

8. ButA charge can be in equilibrium if there are mechanical constraints.

9. conductorsCan a system of charged conductors produce a field that will have a stable equilibrium point for a point charge?

10. The Thompson model of an atom(18 December 1856 – 30 August 1940)

11. The Rutherford model of an atom 30 August 1871 – 19 October 1937

12. The experiment!

13. Thompson’s static model had to be abandoned. Rutherford and Bohr then suggested that the equilibrium might be dynamic ,with the electrons revolving in orbits.

14. The field of a line charge

15. A sheet of charge ; two sheets

16. 2 charged sheets E(outside ) = 0

17. Uniformly charged sphere

18. Is the field of a point charge exactly ? =1

19. The validity of Gauss ’ law depends upon the inverse square law of Coulomb.

20. How shall we observe the field inside a charged sphere? Benjamin noticed that the field inside a conducting sphere is 0 ! Benjamin Franklin (January 17, 1706  – April 17, 1790)

21. The Experiment:

22. The fields of a conductor • The electric field just outside the surface of a conductor Is proportional to the local Surface density of charge.

23. The field in a cavity of a conductor

24. Thanks 4 ur attention

25. In the name of God Chapter 6 By SeyedehSedighehHashemi

26. Chapter 6 May 11, 1918 – February 15, 1988 • The Electric Field in various circumstances

27. Outline Equations of the electrostatic potential The electric dipole Remarks on vector equations The dipole potential as a gradient The dipole approximation for an arbitrary distribution The fields of charged conductors The method of images A point charge near a conducting plane A point charge near a conducting sphere Condensers; parallel plates High-voltage breakdown The field emission microscope

28. Part 1Equation of the electrostatic potential • The whole mathematical problem is the solution of :

29. Poisson equation:

30. Part 2

31. In an insulator the electrons can not move very far . they are pulled back bythe attraction of the nucleus . there is a tiny separation of its + and – charges. And it becomes amicroscopic dipole

32. Water molecule The hydrogen atom s have slightly less Than their share of the electron cloud ; The Oxygen ,slightly more.

35. In dipole potential if “d” is much more than “z”, we can write:

36. The difference of these 2 terms:if and p=qd

37. Dipole moment of 2 charges: Dipolepotential:

38. We wrote the equations in vector form so that they no longer depend on any coordinate system.

39. Part 4 = is the potential of a unit point charge.

40. Two uniformly charged spheres , superposed with a slight displacement , are equivalent to a non uniform distribution of surface charge.

41. Part 5the potential from the whole collection is:

42. for r=R Q is the total charge of the whole object.

43. We need a more accurate expression for rthat is a dipole potential

44. Part 6

45. Part 7

46. feels a force toward the plate:

47. Part 8

48. Part 9

49. Electric field near the edge of two parallel plates

50. The electric field near a sharp point on a conductor is very high