1. First circular accelerator in the world Chap 22-24 Electric field

2. Easy chair Charged hair

3. Electricity and Magnetism  Electric forces hold atoms and molecules together.  Electricity controls our thinking, feeling, muscles and metabolic processes.  Electricity and magnetism underpin much of our current technology (e.g. computers).  Electricity and magnetism are linked on a fundamental level.

4. electric charge electrostatics electron proton neutron nucleus positive ion negative ion ionization conductor insulator point charge Key terms: electric dipole closed surface electric flux surface integral Gauss’s Law Gaussian surface Faraday’s icepail experiment electric potential energy electric potential voltage electron volt equipotential surface gradient cathode-ray tube

5. §1 charges and couloumb’s law 1. 1 charges 1) Negative and positive 2) quantified (millikan) Fraction charge 3) conservation (Franklin) 4) Invariance of charges

6. 1.2 Couloumb’s law 1) Model:point charge 2) Couloumb’s law k=9×10 9 Nm 2 /c 2 ，  0 =8.85×10 -12 c 2 /Nm 2

7. 3) in general Caution: 1)valid for point charge in air 2) obey newton’s law Henry Cavendish Experiment

8. 1. Even though electric forces are very much stronger than gravitational forces, gravitational forces determine the motions in the solar system. Why? 2. When we approach another person, we are not aware of the gravitational and electric forces between us. What are the reason in each case? Quiz

9. §2 Electric field E 2.1 Electric field Electric sourceElectric fieldElectric charge Electric field for point charge Collection of point charge superposition of electric field

10. Charge distribution P Step to solve E:

11. Positive electric charge Q is distributed uniformly along a line with length 2a, lying along the y-axis between y=-a and y=+a. Find the electric field at point P on the x-axis at a distance x from the origin. y x xO Q a -a P

12. Solution:

14. a) This is same as the field of a point charge. b) When a is much larger than x (that is, a>>x), c) Infinite line of charge Discussion: When x is much larger than a (that is, x>>a), Field due to a Power Line

15. A ring conductor with radius a carries a total charge Q uniformly distributed around it. Find the electric field at a point P that lies on the axis of the ring at a distance x from its center. x y O a Q P x

16. Because the symmetry, E y =0. Solution:

17. Discussion: dly z x r R O q PdE  dE x E O x

18. x R O Q x Find the electric field caused by a disk of radius R with a uniform position surface charge density, at a point along the axis of the disk a distance x from its center.

19. Solution:

20. Discussion: If R is much larger than x while (an infinite sheet of charge) The electric field produced by an infinite plane sheet of charge is independent of the distance from the sheet. Thus the field is uniform. Its direction is everywhere perpendicular to the sheet, away from it.

21. Example Sheet 1 Sheet 2 d x Two infinite plane sheets are placed parallel to each other, separated by distance d. The lower sheet has a uniform positive surface charge density, and the upper sheet has a uniform negative surface charge density with the same magnitude. Find the electric field between the two sheets, above the upper sheet, and below the lower sheet.

22. Solution: At all points, the direction of is away from the positive charge of Sheet 1, and the direction of is towards the negative charge of sheet 2.

23. Find the intensity of electric field of dipole in P Solution: Example: Ox P Electric dipole moment P r Along perpendicular bisector

24. Example Solution:to pivot 0 (1) Maximum torque Torque=0 stable (2) (3) Torque=0,not stable equilibrum Find the torque exert on dipole Discussion O

25. § 3 Gauss law Mathematics & Physics & astronomy

26. 3.1 Electric field line 1) rule: The tangent to the field line express the direction of field the density of the line measure the intensity of the field 2) Essence of Electric field 1) originating from the positive to negative ； (2) never intercross ； (3) no close line. +q+q -q-q

27. Field Lines

29. 3.2 flux 1) In uniform field 2) Non uniform field dSdS   EnEn

30. Open surface Concave:positive, Closed surface Outward: positive To closed surface Direction of (1) Discussion

31. 3.3 Guass’s law

32. 1) suppose a point charge is in the center of a sphere surface 2) suppose a point charge is in any interior place of a sphere surface +q+q

33. S +q+q S1S1 S2S2  q outside the surface  many charges q1q1 q2q2 q3q3 q4q4 q5q5  e only related to internal charge Caution: produced by all charges

34. （ separated charges) （ distribution charge) Source field Guass law Meaning:

35. (3) Zero flux does’t mean the zero field. (1) E in Guass’s law is the E in Guassian surface,it is produced by all the charges in the space (2) the flux only depends on the charges inside 4)to moving charge,coulumb’s law don’t work,but guass’s law works Caution:

36. 3.4 Application of guass law: find E A.symmetry distribution of charges B.intensity in guass surface is uniform or piecewise uniform

37. Example:What is the electric flux through a cylindrical surface? The electric field, E, is uniform and perpendicular to the surface. The cylinder has radius r and length L A) E 4/3 p r 3 L B) E r L C) E p r 2 L D) E 2 p r L E) 0

38. Example:In a model of the atom the nucleus is a uniform ball of +e charge of radius R. At what distance is the E field strongest? A) r = 0 B) r = R/2 C) r = R D) r = 2 R E) r = 1.5 R

39. Conclusion: Step to find E with guass law: (1) analysis symmetry (2) from above  guass surface must be closed one  the field point must in guass surface  E is easy to take out from integral function

40. Find the E of the following charged ball with uniform density R + + + + Solution: r r'r' R E O r

41. Find E of infinite long line Solution: From symmetry: r l P

42. E O r

43. Infinite plane or Sheet Charge per unit area  Cm -2. Mirror symmetry about and perpendicular to plane,find E Solution: From symmetry x O ExEx x O ExEx

44. Example: find E R No relation with r r dr r Inversely proportion to r 2 Solution: ?

45. Example:find E in p Solution: (1) fill in the hollow ball (2) E produced by filling parts: P

46. Problem to deal with guass’s law sphere symmetry R mirror symmetry cylindrical symmetry

47. § 4 potential 4.1 work done by electric force Potential energy

48. Discussion: a.conservative force b.potential of point charge c.potential difference

49. (1) belong to q 0 and field source Caution: (3) rule for choose zero potential energy (2) with related value in practice,earth and the out shell of equipment when sources is limited,choose infinite place in contrary, a specific place is choose

50. 1)potential of charged particle 3 、 the calculation of potential 2)collection of charge particles: 3)continuous charge distribution 4.2 calculation of potential

51. Find the potential of dipole Solution: r>>l ，

52. Example:find potential of rod with l=15.0cm, =2.0  10 -7 c/m (2) in perpendicular bisector x dx a P l x y l Solution: (1)

53. solution ： 1) x O Ｕ In center dly z x r R O q PdE  dE x Example:Find potential in axis

54. § 5 relationship between field and potential 5.1 basic concept Equivalent potential surface ： (2)the density of equal potential surface reflect the intensity of electric field. (3)the direction of the line of force is the descended direction of potential (1) Character:

55. 5.2 the relation between electric field and potential Negative of the gradient of U

56. Example:find the E and U of the following disk Solution: take a circular strip P ExEx x dr r R1R1 R2R2