## Permanent Magnet and Electromechanical Devices: Materials, Analysis, and ApplicationsThe book provides both the theoretical and the applied background needed to predict magnetic fields. The theoretical presentation is reinforced with over 60 solved examples of practical engineering applications such as the design of magnetic components like solenoids, which are electromagnetic coils that are moved by electric currents and activate other devices such as circuit breakers. Other design applications would be for permanent magnet structures such as bearings and couplings, which are hardware mechanisms used to fashion a temporary connection between two wires. This book is written for use as a text or reference by researchers, engineers, professors, and students engaged in the research, development, study, and manufacture of permanent magnets and electromechanical devices. It can serve as a primary or supplemental text for upper level courses in electrical engineering on electromagnetic theory, electronic and magnetic materials, and electromagnetic engineering. |

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### Contents

Materials | 1 |

12 Units | 2 |

13 Classification of Materials | 6 |

14 Atomic Magnetic Moments | 7 |

141 Single Electron Atoms | 9 |

142 Multielectron Atoms | 14 |

15 Paramagnetism | 17 |

16 Ferromagnetism | 19 |

37 Method of Images | 185 |

38 Finite Element Analysis | 190 |

39 Finite Difference Method | 200 |

Permanent Magnet Applications | 207 |

42 Magnet Structures | 208 |

422 Cylindrical Structures | 218 |

43 High Field Structures | 265 |

44 Magnetic Latching | 268 |

17 Magnetocrystalline Anisotropy | 23 |

19 Anisotropy | 27 |

192 Shape Anisotropy | 31 |

110 Domains | 33 |

111 Hysteresis | 36 |

112 Soft Magnetic Materials | 39 |

113 Hard Magnetic Materials | 44 |

114 Ferrites | 46 |

115 Alnico | 48 |

116 SamariumCobalt | 50 |

117 NeodymiumIronBoron | 51 |

118 Bonded Magnets | 53 |

119 Magnetization | 55 |

120 Stability | 66 |

Review of Maxwells Equations | 73 |

22 Maxwells Equations | 74 |

221 Constitutive Relations | 75 |

222 Integral Equations | 77 |

223 Boundary Conditions | 79 |

224 Force and Torque | 82 |

24 Quasistatic Theory | 85 |

25 Static Theory | 87 |

252 Electrostatic theory | 89 |

26 Summary | 91 |

Field Analysis | 97 |

321 Vector Potential | 102 |

322 Force and Torque | 110 |

323 Maxwell Stress Tensor | 112 |

324 Energy | 116 |

325 Inductance | 118 |

33 The Current Model | 126 |

34 The Charge Model | 131 |

341 Force | 135 |

342 Torque | 141 |

35 Magnetic Circuit Analysis | 144 |

352 Magnet sources | 153 |

36 BoundaryValue Problems | 161 |

361 Cartesian Coordinates | 162 |

362 Cylindrical Coordinates | 175 |

363 Spherical Coordinates | 180 |

45 Magnetic Suspension | 273 |

46 Magnetic Gears | 282 |

47 Magnetic Couplings | 286 |

48 Magnetic Resonance Imaging | 306 |

49 Electrophotography | 312 |

410 Magnetooptical Recoriding | 318 |

411 FreeElectron Lasers | 325 |

Electromechanical Devices | 335 |

53 QuasiStatic Field Theory | 337 |

531 Stationary Reference Frames | 338 |

532 Moving Reference Frames | 341 |

54 Electrical Equations | 354 |

542 Moving Coils | 358 |

55 Mechanical Equations | 361 |

56 Electromechanical Equations | 363 |

562 Moving coils | 366 |

57 Energy Analysis | 376 |

58 Magnetic Circuit Actuators | 383 |

59 AxialField Actuators | 393 |

510 Resonant Actuators | 402 |

511 Magnetooptical Bias Field | 406 |

512 Linear Actuators | 413 |

513 AxialField Motors | 421 |

514 Stepper Motors | 437 |

515 Hybrid AnalyticalFEM Analysis | 446 |

516 MAGNETIC MEMS | 455 |

Vector Analysis | 469 |

A2 Cylindrical Coordinates | 473 |

A3 Spherical Coordinates | 476 |

A4 Integrals of Vector Functions | 479 |

A5 Theorems and Identities | 485 |

A6 Coordinate Transformations | 491 |

Greens Functions | 495 |

Systems of Equations | 497 |

C1 Eulers Method | 498 |

C2 Improved Euler Method | 502 |

C3 RungeKutta Methods | 503 |

Units | 509 |

513 | |

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### Common terms and phrases

2ero actuator alignment Alnico analysis analytical angular anisotropy apply Eq Assume atomic axial axial-field axis B-field bias field boundary conditions charge coefficients coil computed conductor consider constant constitutive relations coupling current density demagnetixation curve denote derived determine dipole domain electrical electromagnetic electromechanical devices electron element energy Euler's method example Exampt.e external field ferromagnetic field components field equations field solution FIGURE flux linkage flux plate function Furlani geometry given by Eq inductance integral interface length linear motion magnetic circuit magnetic field magnetic materials magnetic moment magnetixation magnetostatic magnetostatic field Maxwell stress tensor Maxwell's equations mechanical method motor NdFeB Notice obtain orientation permanent magnet permeability polarixed potential radial radius reduces reference frame respectively rotational motion rotor Runge-Kutta method second quadrant Section segments shown in Fig soft magnetic Specifically specimen stationary stator stepper motor Substitute Eq torque variables vector voltage volume wiggler wire xero