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CH6 Static Magnetic Field

CH6 Static Magnetic Field. Electric force Magnetic force Elecmagnetic fore. (N) ~ Lorentz’s force equation. Static Electric Field. Static Magnetic Field. Free space. Steady current. Permeability of free space. No magnetic flow sources Magnetic flux lines always close

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CH6 Static Magnetic Field

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  1. CH6 Static Magnetic Field

  2. Electric force • Magnetic force • Elecmagnetic fore (N) ~ Lorentz’s force equation

  3. Static Electric Field Static Magnetic Field Free space Steady current Permeability of free space

  4. No magnetic flow sources • Magnetic flux lines always close • Low of conservation of magnetic flux • Each magnets has a north south • Magnetic poles cannot be isolated pole

  5. Ampere’s circuital law summary

  6. EX 6-1 • Inside conductor • Outside conductor C2 outside conductor encloses I

  7. b If 空心圓柱(柱座標)

  8. EX 6-2 (Toroidal Coil) A circular contour C with radius r (b - a) < r < (b + a) (b - a) < r < (b + a) (No source)

  9. (a) Direct application of Ampere Law (b) Special case of torid Ex 6-2, EX 6-3 (Solenoid Coil)

  10. 6-3 Vector Magnetic Potential : magnetic potential [Vector] c.f : electric potential [Scalar] 取 Vector Poisson’s equation Coulomb gauge

  11. In Cartesian coordinates, Vector

  12. Magnetic Flux through a given area S which is bounded by contour C

  13. 6-4 Biot-Savart Law and applications Vector source Magnetic: Current distribution Current element

  14. 0 Biot-Savart Law：[Valid in steady current] 0 c.f. 因次分析

  15. Biot-Sarvart Law： Action at a distance： field

  16. Gauss thm. 特殊式 Biot-Sarvart Law Poission Eqe. Stoke Thm. Ampere’s Law

  17. PF: =0 =0 N 封閉磁迴路 S C.F 孤立電單極

  18. From 0 其中

  19. From Steady current Static magnetic field 其中： Steady state Coulomb Gauge

  20. 其中： Ampere’ Law Poission Equ.

  21. Gauss Thm.

  22. Example 6-4 (a)

  23. Example 6-5 From 6-4

  24. Example 6-6 is canceled due to cylindrical sym.

  25. 6-5 Magnetic Dipole 2’ pole = 0 20 pole = 0

  26. c.f.

  27. c.f.

  28. Scalar Magnetic Potential : Scalar Magnetic Potential (not physical) : Non conservative (path dependent)

  29. 磁性物質 Components source Conductor free electron Non-conductor polarized ion 6-6 Magnetization and Equivalent Current Density 定義

  30. c.f.

  31. EX : 6-8

  32. 靜磁學 (包含導體與磁性材料) C.F.

  33. Static Magnetic Source : (permeativity) Conductor : Magnetic material : Copy 電學 數學上等效，無物理

  34. Ex 6-9 電場 與（Dipole 類似）

  35. 6-7 Ampere’s circuital law ; relative permeability

  36. 6-8 Magnetic Circuits Electric circuit : Voltage / Current source ; V, I, … Magnetic circuit : Transformer / Generator / Motor … ; closed path c to enclose N turns of I (m.m.f) magnetomotive force [Amp]

  37. Ex 6-10 Sol : is identical in different material ; f : ferromagneticg : gap Ampere law

  38. Magnetic Flux ; S : cross-section : length of ferromagnetic core. :ferromagnetic core :air gap : Reluctance Analog to : [Electric circuit]

  39. Magnetic circuit Electric circuit mmf mag. flux reluctance Permeability emf electric current , resistance , conductivity ,

  40. An exact analysis of magnetic circuits is difficult ◎Leakage Fluxes ◎Fringing effect ◎ 2 conditions must be satisfied Similar to Kirchhoff’s voltage Law Kirchhoff’s current Law

  41. EX.6-11 K.V.L. (Time Independent) Loop1: Loop2:

  42. 6-9 Behavior of Magnetic Materials ◎Diamagetic: ◎Paramagnetic: ◎Ferromagnetic:

  43. 6-10 Boundary Conditions for Magnetostatic Field

  44. Ex 6-12 Bn component component or Similar to E-field Magnitude of In ferromagnetic parallel interface Originates in a ferromangeitc , Flux perpendicular to interface

  45. Ex 6-13 Surface current Example 6-8 [p246] Center End at interface quantity

  46. 6-11 Inductances & Inductors Mutual flux ： mutual inductance between loops C1 and C2 If loop C2 has N2 turns , Generalizes to

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