1. Ch2. 靜電學(Electrostatics)
2.1 電場(The Electric Field)
2.2 靜電場的發散與旋度(Divergence and Curl of Electrostatic Fields)
2.3 電位(Electric Potential)
2.4 靜電學中的功與能量(Work and Energy in Electrostatics)
2.5 導體(Conductors)

2. 2.1.1 電場(The Electric Field)

3. 2.1.2 庫倫定律(Coulomb’s Law) Q Q
Charles Coulomb 1785 : fundamental law of electric force between two stationary charged particles. The force is:
inversely proportional to square of the distance between the particles,
directed along the line joining the particles,
proportional to the product of the two charges and
attractive if particles have charges of opposite sign and repulsive if charges have same sign. Q 2 Q 1

4. 2.1.3.1 電場(The Electric Field)
Source point
Field point
The far right term

5. 2.1.3.2 電場(The Electric Field)
Example : Electric dipole
Because y >> a, we neglect a2 and write

6. 2.1.4.1 連續電荷分佈(Continuous Charge Distributions)
Source : a line charge
Source : a surface charge
Source : a volume charge

7. 2.1.4.2 連續電荷分佈(Continuous Charge Distributions)
Example :
A rod of length l has a uniform charge per unit length λand a total charge Q. Calculate the electric field at a point P along the axis of the rod at a distance a from one end. Note that λ= Q/l.
Uniform positive charge per unit length 
If a >>

8. 2.1.4.3 連續電荷分佈(Continuous Charge Distributions)
Example : Electric Field of a Uniform Ring of Charge
If x >> a

9. 2.1.4.4 連續電荷分佈(Continuous Charge Distributions)
Example : Electric Field of a Uniformly Charged Disk
If R >> x

10. 2.1.4.5 連續電荷分佈(Continuous Charge Distributions)
Example : Electric Field of an Infinite Plane of Charge

11. 2.1.4.6 連續電荷分佈(Continuous Charge Distributions)
Example : Electric Field Between Two Oppositely Charged Parallel Plates

12. 2.1.4.7 連續電荷分佈(Continuous Charge Distributions)
Example 2.1
Find the electric field a distance z above the midpoint of a straight line segment of length 2L, which carries a uniform line charge .  r
dx 2L

13. 2.1.4.8 連續電荷分佈(Continuous Charge Distributions)
Problem 2.4
Find the electric field a distance z above the center of a square loop (side a) carrying uniform line charge . z
Remember example 2.1 a
Field of one edge is :
For four sides :

14. Point away from positive charge Point towards negative charge
場線(Field Lines) E E
+ q
- q
Point away from positive charge
Point towards negative charge

15. 場線(Field Lines)
場線規則
1. Field lines always begin on positive charges and end on negative charges. (In doing so, they may leave and re-enter the picture frame).
2. The (net) number of lines exiting or entering a charge is proportional to the charge magnitude.
3. The density of lines (number of lines per unit area through a surface perpendicular to the lines) is proportional to the field strength there.
4. At any point, the direction of a field line (its tangent) is the direction of the electric field vector E at that point.
5. Field lines, representing the total E field, never cross one another.
6. Field lines very close to a point charge are distributed symmetrically.

16. 2.2.1.3 場線(Field Lines) •Electric field lines are not material objects+q +q -q +q
•Electric field lines are not material objects
•Finite number of lines can be misleading
•The electric field is continuous and exists at every point
•The electric field is three dimensional

17. 通量(Flux)

18. 通量(Flux)

19. 通量(Flux)

20. 高斯定律(Gauss’s Law)

21. 2.2.1.8 高斯定律(Gauss’s Law) Divergence theorem :
Gauss’s law in differential form

22. 2.2.1.9 高斯定律(Gauss’s Law) Problem 2.9
Suppose the electric field in some region is found to be , in spherical coordinates (k is some constant).
(a). Find the charge density .
(b). Find the total charge contained in a sphere of radius R, centered at the origin. or

23. 2.2.2 電場的發散(The Divergence of E)
Source point
Field point

24. 2.2.3.1 高斯定律的應用(Application of Gauss’s Law)

25. 2.2.3.2 高斯定律的應用(Application of Gauss’s Law)

26. 2.2.3.3 高斯定律的應用(Application of Gauss’s Law)

27. 2.2.3.4 高斯定律的應用(Application of Gauss’s Law)

28. 2.2.3.5 高斯定律的應用(Application of Gauss’s Law)

29. 2.2.3.6 高斯定律的應用(Application of Gauss’s Law)
Example 2.3 s
Find the electric field inside this cylinder

30. 2.2.4.1 電場的旋度(The Curl of E) Consider a point charge at the origin : z
If we calculate the line integral of this field rb q y ra x
In spherical coordinates :

31. 電場的旋度(The Curl of E)
For the integral around a closed path (ra = rb) :
史托克定理(The Stokes’ theorem)

32. 2.3.1 電位的介紹(Introduction to Potential)

33. 2.3.1 電位的介紹(Introduction to Potential)
Since we will only ever calculate differences in potential, the value of the potential at the reference point O can be anything as long as it is finite. Therefore, we can simply define the electric potential at a point P(x,y,z) as:
Normally, the reference point is at infinity where V=0. In fact, V is not physical (charges can’t feel it directly). It only becomes physical once you take its gradient to form E.

34. 2.3.1 電位的介紹(Introduction to Potential)
V obeys the superposition principle

35. 2.3.1 電位的介紹(Introduction to Potential)
Equipotential surface
surface

36. 2.3.2 關於電位的重點

37. 2.3.2 關於電位的重點

38. 2.3.2 關於電位的重點

39. 2.3.2 關於電位的重點

40. 2.3.3 Poisson’s Equation and Laplace’s Equation

41. 2.3.4 一個局域電荷分佈的電位(The Potential of a Localized Charge Distribution)

42. 2.3.4 一個局域電荷分佈的電位(The Potential of a Localized Charge Distribution)

43. 2.3.4 一個局域電荷分佈的電位(The Potential of a Localized Charge Distribution)

44. 2.3.4 一個局域電荷分佈的電位(The Potential of a Localized Charge Distribution)

45. 2.3.4 一個局域電荷分佈的電位(The Potential of a Localized Charge Distribution)

46. 2.3.4 一個局域電荷分佈的電位(The Potential of a Localized Charge Distribution)
E=0 inside conductor in equilibrium. Any net charge resides on the surface of the conductor. Electric field immediately outside the conductor is perpendicular to the surface of the conductor.
Consider the two points A and B on the surface of the charged conductor. Along a surface path connecting these points E is always perpendicular to ds.
V is constant everywhere on the surface of a charged conductor in equilibrium. Since electric field inside the charged conductor in equilibrium is zero, the potential is constant everywhere inside the conductor and equal to its value at the surface.

47. 2.3.5 總結; 靜電的邊界條件(Summary; Electrostatic Boundary Conditions)

48. 2.3.5 總結; 靜電的邊界條件(Summary; Electrostatic Boundary Conditions)

49. 2.3.5 總結; 靜電的邊界條件(Summary; Electrostatic Boundary Conditions)

50. 2.3.5 總結; 靜電的邊界條件(Summary; Electrostatic Boundary Conditions)

51. 2.3.5 總結; 靜電的邊界條件(Summary; Electrostatic Boundary Conditions)

52. 2.3.5 總結; 靜電的邊界條件(Summary; Electrostatic Boundary Conditions)

53. 2.4.1 移動一電荷所做的功(The Work Done to Move a Charge)

54. 2.4.2 一個點電荷分佈的能量(The Energy of a Point Charge Distribution)

55. 2.4.3 一個點電荷分佈的能量(The Energy of a Point Charge Distribution)

56. 2.4.4 一個點電荷分佈的能量(The Energy of a Point Charge Distribution)
Problem 2.31
(a). -q +q
(b)

57. 2.4.5 一個連續電荷分佈的能量(The Energy of a Continuous Charge Distribution)

58. 2.4.6 一個連續電荷分佈的能量(The Energy of a Continuous Charge Distribution)

59. 2.4.7 一個連續電荷分佈的能量(The Energy of a Continuous Charge Distribution)
The integral above contains self-energy terms and interaction energy terms. The former are always positive (and generally large), whereas the latter can be positive or negative.
Example: Consider two point-like charges q1 and q2 at some non-zero separation. Calculate the interaction energy using the summation form and either of the integral forms above

60. 2.4.8 一個連續電荷分佈的能量(The Energy of a Continuous Charge Distribution)
interaction energy terms

61. 2.5.1 導體的基本性質

62. 2.5.2 導體的基本性質

63. 2.5.3 導體的基本性質

64. 2.5.4 導體的基本性質
(a).
(b).
(c).

65. 2.5.5 在一導體上的表面電荷與力(Surface Charge and the Force on a Conductor)

66. 2.5.6 在一導體上的表面電荷與力(Surface Charge and the Force on a Conductor)
The force per unit area on a conductor :
The electrostatic pressure :

67. 2.5.7 電容器(Capacitors)

68. 2.5.8 電容器(Capacitors)

69. 2.5.9 電容器(Capacitors)

70. 電容器(Capacitors)

71. 電容器(Capacitors)

72. 電容器(Capacitors)

73. 電容器(Capacitors)