Volume 2

1. Volume 2 Electromagnetism Study the properties and laws of electric field, magnetic field and electromagnetic field that they are stimulated by charges and currents.

3. stimulated by static charges with respect to observer. Inertial reference frame Chapter 8 Electrostatic Field in Vacuum

4. §8-1 Coulomb’s Law 库仑定律 §8-2 The Electric Field 电场 电场强度 §8-3 Electric Field Line and Flux 电力线 电通量 §8-4 Gauss’ Law 高斯定理 §8-5 Electric Potential 电势 §8-6 Equipotential Surface and Potential Gradient 等势面 电势梯度 §8-7 The Electric Force Exerted on a Moving Particle 运动带电粒子所受电场力

5. §8-1 Coulomb’s Law 1. Two kinds of electric charges positive charge Negative charge Like charges repel each other Unlike charges attract each other

6. integer 2. quantization of charge experiments show： Electron is the smallest negative charge in nature. Proton is the smallest positive charge in nature. e=1.60217733×10-19 C(Coulomb) The magnitude of electric charge possessed by a body is not continuous. q= Ne

7. 3. Conservation of charge  Electrification by rubbing Positive charges and negative charges havesame magnitude.

8. Electrification by induction： inducible charges have same magnitude.

9. The conservation of charge：in any interaction the net algebraic amount of electric charge remains constant.

10. 4. Coulomb’s Law  Point charge： The size of charged bodies << their distance  Coulomb’s Law： or

11. In SI ： 0=8.8510-12 C2/Nm2 ----permittivity of vacuum（真空介电系数）

12. 5. Superposition principle of electrostatic forces Assume there are many point charges in space:q0、 q1、 q2、q3…qn， the resultant force acting on q0 : ---vector addition

13.  charge charge  charge field charge Field is a kind of matter. 1.Viewpoints of the interaction about electric charges  Viewpoint of action-at-a distance: §8-2 The Electric Field  Viewpoint of field:

14. The behavior of electric field as a kind of matter:  force：E-field exerts a force on the charges in it.  work：E-field does work on charges during the charges move in it.  induction and polarization： in the field,conductor and dielectric produce induction and polarization.

15. Test charge:  small size--point charge  small charge magnitude—no influence for original field. 2. Electric field Test results:  same q0 is put on different points in space,

16. the direction and the magnitude of the force that q0 suffers is different at different points ---E-field is different at different points  Put different test charges on same point, the electricforces that the test charges suffer change. the ratio =constant vector at same point.

17.  the electric field is defined： SI unit：牛顿/库仑 (N/C) or伏特/米 (V/m)

18. 3. the superposition principle of electric field There are q1、q2、q3 … qnin space, q0 is put on the point P, the force acting on q0 : At point P, the E-field is set up byq1、q2、q3 … qn:

19. 4. The distributions of electric field about several different charged bodies .point charge: Put qoon point P，using Coulomb Law，qo suffers --the E-field of a point charge

20. The distribution is spherical symmetry

21. P .the point charge system There are q1，q2，…, qn in space Each charge set up its field at point P：

22. the total field at P：

23. .A continuously distributed charged body At point P, element chargedq produces: The total field at P produced by entire charged body:

24. line distribution area distribution volume distribution  According to the distribution of charge, dqis written as follow:  for Cartesian coordinate system ：

25.  write out produced by dq at point P  set up a coordinate system, write components of , such as 5. Examples of calculating E-field Steps：  divide charged body into many small charge elements .

26.  calculate the components of , such as  total E-field

27. P d 2 1 l q [Example] Calculate the E-field at point P produced by a charged line. L、q、d、1、 2are known

28. . Any dq produces at P The magnitude of : P The direction of shows in Fig. d 2 1 r dq l q Solution . divide q  dq

29. y P d  2 1 o r x dq l q . set up Cartesian coordinate, . calculate Ex、Ey

31. y P d  2 1 o r x dq l q In the figure：

32. . the total Same as

33. Discussion （1）If P locates on the mid-perpendicular plane of the line, i.e.

34. （2）If P isveryclose to the line 、 --the length of the charged line tends to infinity E-field distribution of the infinite line with uniform charge

35. （3）If P is far away from the line The charged line can be regarded as a point charge.

36. q P l a Question：If P locates on the elongating line of the charged line shown as in figure, How do we calculate Ex、Ey ?

37. directly, use only for point charge. (2) If the directions of for different are not same, we can not integrate directly. integrating its components Caution！ (1) If the charged body is not a point charge, we can not use the formula

38. r R q q · x x P [Example] Find the E-field of an uniform charged ring on its axis. （q、R、xare known)

39. dq Divideq dq r R q q · x x P direction Solution

40. Direction: along xaxis

41. let Discussion （1）at x=0，E=0. When x  ， E has extreme values on x axis. We get （2）when x>>R， can be regarded as a point charge.

42. E 0 x

43. [Example] thin round plate with uniform charge area density, radius R. find its field on the axis.

44. discussion （1）when x « R , The E-field set up by uniform sheet charge of a infinite plane. （2）when x » R , as a point charge

45. §8-3 Electric field line and flux the tangential direction of line at any point gives the direction of at that point. 1. E-field line（ line） the density of line gives the magnitude of --area element perpendicular to line. de – the number of line crossing .

46. The properties of line. line originate on positive charges and terminate on negative charges (or go on infinity). They never originate or terminate on a no-charge point in finite space. Two lines never intersect at a point. 2. Electric flux – the number of line crossing any area.

47.  The plane S is at any angle with :the unit vector at the normal direction of the plane.   The plane S is at right angle to the uniform E-field.

48. An arbitrary surfaceS is placed in a no-uniform E-field. Take any dS on S : The total E-flux crossing S：

49. Stipulation：the direction of is outward. n de< 0 E de >0 If S is a closed surface：

50. If there is no any charge in the closed surface, the number of line entering it equals the number of line going out it. If there are charges in the closed surface, the number of line entering it does not equal the number of line going out it. relate to the charge in the surface.