10 電磁 III

1. 10 電磁 III How is an aurora so thin yet so tall and wide?

2. Sections • 磁場 • 電流與磁場

3. 10-1 磁場 • The electric field and the magnetic field • Electromagnets and permanent magnets

4. 10-1.1 The definition of B

5. The tracks in a bubble chamber

6. The SI unit for B 1 tesla = 1T =1 N/A‧m=104 gauss 108 T 1.5 T 10-2 T 10-4 T 10-10 T 10-14 T

7. Magnetic Field Lines • Magnetic vs. electric dipoles

8. A horseshoe and a C-shaped magnets

9. 例 1 A 5.3 MeV proton B = 1.2 mT

10. 10-1.2 Crossed Fields: Discovery of the Electron • A cathode ray tube • Thomson’s procedure: • 設定E = 0, B = 0, 並記錄光點位置 • 開啟電場 • 開啟磁場,並調至與電場相等

11. Calculation the charge-to-mass ratio of the electron 1.75881961011 C·kg-1

12. 10-1.3 Crossed Fields: The Hall Effect • By the conduction electrons in copper:

13. 例 2 A cube generator d = 1.5 cm, v = 4.0m/s, B = 0.05T

14. 10-1.4A Circulating Charged Particle

15. 頻率與軌跡 The frequency and angular frequency The magnetic bottle machine

16. Helical Paths V∥ and V⊥ The pitch (螺距) of the helical path

17. 極光橢圓圈

18. 例 3 The Mass Spectrometer (質譜儀)

19. 質譜儀 x = 1.6254m, V = 1000.0V, B = 80.000mT Isotope Separation Centrifuge and diffusion chamber

20. 10-1.5Cyclotrons and Synchrotrons (迴旋加速器與同步加速器) Fermilab: 6.3km ring

21. Synchrotrons • The resonance condition: • When proton energy > 50Mev: • Out of resonance (relativistic effect) • A huge magnet (4×106 m2) is needed for high energy (500Gev) protons • The proton sychrotron at Fermilab can produces 1Tev proton

22. CERN LHC The LHC is 27km long and sits 100m below the surface.

23. 10-1.6Magnetic Force on a Current-Carrying Wire

24. Magnetic Force For a wire segment:

25. 例 4 A length of wire with a semicircular arc

26. Calculation

27. 線圈

28. 10-1.7Torque on A Current Loop • F2 and F4 cancel • F1 and F3 form a force couple

29. 例 5 A galvanometer for analog meters

30. 10-1.8The Magnetic Dipole • The magnetic dipole moments • The magnetic potential energy

31. 磁能

32. 10-2 Magnetic Fields due to Currents Conventional rocket EM Rail Gun

33. 1 dq = dE pe 2 4 r 0 v 1 dq v = d E r pe 3 4 r 0 m q ids sin = 0 dB p 2 4 r v v m  id s r = 0 dB p 3 4 r 10-2.1 Calculating the Magnetic Field due to a current The law of Biot and Savart

34. Magnetic Field Due to a Current in a Long Straight Wire

35. Integration

36. Magnetic Field Due to a Current in a Circular Arc of Wire

37. 例 6 What B does the current produce?

38. 10-2.2 Two Parallel Currents

39. 例 7 The Field Between Two wires

40. 10-2.3 Ampere’s Law • Comparing Gauss’ law and Ampere’s law • Ampere’s law

41. The Magnetic Field Outside a Long Straight Wire with Current

42. The Magnetic Field Inside a Long Straight Wire with Current

43. 例 7 A hollow conducting cylinder

44. 10-2.4 Solenoids and Toroids • Magnetic Field of a Solenoid (螺線管) • Magnetic Field of a Toroid (螺線環)

45. Magnetic Field of a Solenoid

46. Magnetic Field of a Toroid

47. 磁圍阻核融合反應器 Tokamak Fusion Test Reactor

48. 10-2.5 A Current Carrying Coil as a Magnetic Dipole • A current loop and a bar magnet

49. Magnetic Field of a Coil

50. Coulomb’s Law • Using Gauss’s law to take advantage of special symmetry situations • Gaussian surfaces • 高斯面上各點電場與面內總電荷相關