## Magnetic and Electromagnetic Shielding |

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### Contents

INTRODUCTORY REMARKS | 1 |

MAGNETIC SHIELDING | 5 |

22 Magnetic Shielding by Spherical Shells | 6 |

2212 Magnetic lines of force | 10 |

2213 Thick and thin shells | 15 |

2215 Magnetic field arising from a shell having a remanent magnetization | 19 |

222 Multiple shells | 28 |

2221 Theory for multiple shells | 29 |

341 Electromagnetic induction by a magnetic field arising from outside a cylindrical shell | 131 |

342 Shielding effect to an external field | 134 |

35 Square and Octagonal Shells of Infinite Length | 137 |

352 Application of the relaxation method | 139 |

3532 Square shell | 142 |

3533 Square shell in a magnetic field in a direction which makes an angle of 45 with the shell wall | 144 |

3534 Octagonal shell | 146 |

36 Thin Sheet or Shell | 149 |

2222 How efficient is a system of multiple shells? | 32 |

2223 Magnetic lines of force and their density | 35 |

2224 Optimal model of multiple shells for shielding | 36 |

23 Magnetic Shielding by Cylindrical Shells | 38 |

231 Cylindrical shell of infinite length | 40 |

232 Cylindrical shell of finite length | 44 |

2321 External magnetic field parallel to the cylinder axis | 45 |

2322 External magnetic field perpendicular to the cylinder axis | 63 |

2323 Summary of magnetic shielding by cylindrical shells of finite length | 86 |

24 Magnetic Shielding by Rectangular Shells of Infinite Length | 88 |

2411 Relaxation | 89 |

242 Solid and hollow prisms | 94 |

243 Incomplete square shell | 102 |

ELECTROMAGNETIC SHIELDING | 107 |

31 Fundamental Equations | 108 |

32 Plane Slab | 110 |

321 Line of magnetic dipoles over a uniform slab | 117 |

33 Spherical Shell | 120 |

332 Electromagnetic induction by a magnetic field arising from outside a spherical shell | 121 |

333 Shielding effect to an external field | 124 |

334 Electromagnetic induction by a magnetic field arising from inside a spherical shell | 127 |

335 Shielding effect to an internal field | 130 |

362 Plane sheet | 154 |

363 Cylindrical sheet | 156 |

364 Spherical sheet | 158 |

365 Hemispherical sheet | 161 |

366 Square sheet | 162 |

37 Shielding by Two Concentric Spherical Shells One Electrically Conducting the Other Magnetically Permeable | 164 |

371 Model 1 | 167 |

372 Model 2 | 170 |

373 Comparison of shielding power between Models 1 and 2 | 171 |

38 TwoLayer Conductor | 172 |

382 Plane layer model | 179 |

383 Spherical layer model | 183 |

384 Cylindrical layer model | 189 |

385 Negis negative screening | 193 |

ELECTROMAGNETIC INDUCTION IN A NONUNIFORM SHEET | 197 |

MAGNETIC SHIELDING BY A PLANE SLAB | 207 |

ELECTROMAGNETIC SHIELDING BY A PLANE SLAB WHEN IT IS UNDERLAIN BY A CONDUCTOR FROM WHICH THE INDUCING FIEL... | 210 |

ELECTROMAGNETIC RESPONSE OF TWOLAYER SPHERICAL MODEL | 214 |

223 | |

225 | |

SUBJECT INDEX | 227 |

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### Common terms and phrases

becomes boundary conditions calculated Changes in mod component of magnetic conducting shell current function curves cylinder axis defined degree of shielding difference equation distribution of magnetic electric currents electrical conductivity electromagnetic induction electromagnetic response electromagnetic shielding external field external magnetic field figure free space given Grid points highly-permeable inducing field induction parameter infinite length inner conductor inner radius lines of force magnetic field arising magnetic field components magnetic flux density magnetic flux function magnetic lines offorce magnetic permeability magnetic potential model shown multiple shells normal component obtain outer layer outer radius perpendicular plane slab problem relaxation method rewritten RIKITAKE rz plane satisfies shell model shell of infinite shell wall shielding effect shielding power shielding ratio shown in Fig similar single shell Solving spherical shell square shell tangential component theory of electromagnetic thin sheet two-layer model typical solution uniform magnetic field values vector potential wavelength z=0 plane