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Magnetic Fields and Aurora Phenomena Explained

Explore the thin yet extensive nature of auroras through theories of magnetic fields, electric currents, and magnetism. Understand the implications of magnetic dipole moments, Biot-Savart law, Ampere's Law, and applications like cyclotrons and LHC. Delve into the mysteries of magnetic forces on current-carrying wires, torque on current loops, and the magnetic potential energy. Unveil the secrets behind magnetic fields in various scenarios, such as solenoids, toroids, and magnetic dipole interactions, shedding light on phenomena like the Hall Effect and Mass Spectrometer. Unravel the complexities of electromagnetism and its pivotal role in shaping our universe.

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Magnetic Fields and Aurora Phenomena Explained

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  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

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