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1 A Mathematical Introduction |
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1 | (66) |
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1.1 Coordinate Systems and Transformations |
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1 | (3) |
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1.2 Differential Length, Area and Volume |
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4 | (1) |
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1.3 Scalar and Vector Fields |
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5 | (1) |
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1.4 Concept and Definition of Regions, Curves and Surfaces |
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6 | (3) |
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1.5 Line, Surface and Volume Integrals. Circulation and Flux |
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9 | (2) |
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11 | (2) |
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13 | (1) |
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14 | (1) |
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1.9 Stokes's Theorem and Divergence Theorem |
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15 | (1) |
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1.10 Normal Vector to a Surface |
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16 | (3) |
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1.10.1 Vectorial or Parametric |
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16 | (1) |
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17 | (1) |
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17 | (2) |
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1.11 Further Developments |
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19 | (2) |
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1.12 Classification of Vector Fields |
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21 | (2) |
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1.13 Obtaining the Scalar Potential |
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23 | (3) |
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23 | (1) |
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24 | (1) |
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25 | (1) |
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1.14 Vectorial Field from the Vector Potential |
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26 | (41) |
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26 | (2) |
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28 | (1) |
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29 | (1) |
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29 | (22) |
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51 | (16) |
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2 Static Electric Field in Vacuum |
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67 | (54) |
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67 | (1) |
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68 | (2) |
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70 | (1) |
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2.4 Electrostatic Potential |
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71 | (2) |
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2.5 Flux of Electric Field. Gauss' Law |
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73 | (1) |
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2.6 Electrostatic Equations |
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74 | (1) |
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74 | (1) |
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2.8 Conductors and Insulators |
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75 | (1) |
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2.9 Biot--Savart-like Law in Electrostatics |
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76 | (45) |
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77 | (1) |
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77 | (4) |
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81 | (25) |
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106 | (15) |
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3 Static Electric Field in Dielectrics |
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121 | (44) |
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121 | (2) |
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123 | (1) |
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123 | (2) |
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3.4 The Constitutive Equation |
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125 | (2) |
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127 | (1) |
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3.6 Coefficients of Potential and Capacitance |
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128 | (1) |
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129 | (36) |
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132 | (1) |
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132 | (7) |
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139 | (17) |
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156 | (9) |
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165 | (58) |
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4.1 Current Density. The Current |
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165 | (2) |
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4.2 The Equation of Continuity |
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167 | (1) |
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167 | (1) |
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168 | (1) |
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4.5 Ohm's Law in a Conducting Straight Wire. Resistance |
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169 | (2) |
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4.6 Power Supplied by Electric Field. Joule's Law |
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171 | (1) |
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4.7 Direct Current Generators |
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172 | (2) |
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4.8 Direct Current Motors |
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174 | (1) |
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4.9 Ohm's Law in Circuits |
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175 | (2) |
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4.10 Direct Current Networks |
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177 | (2) |
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4.10.1 Kirchhoff's Circuit Laws |
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177 | (2) |
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179 | (1) |
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4.11 Passive Network Equivalence |
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179 | (5) |
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4.11.1 Resistances in Series, Parallel, Triangle and Star Associations |
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180 | (2) |
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4.11.2 Resistance in a Conductor with Any Shape |
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182 | (2) |
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4.12 Thevenin's and Norton's Theorems |
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184 | (39) |
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185 | (1) |
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185 | (9) |
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194 | (12) |
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206 | (17) |
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223 | (90) |
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5.1 Differential Equation of the Magnetostatic Field |
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223 | (2) |
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5.2 Integral Form of the Equations |
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225 | (2) |
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227 | (2) |
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229 | (1) |
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230 | (1) |
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231 | (1) |
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5.7 Off-Axis Magnetic Field for Axisymmetric Systems |
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231 | (82) |
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234 | (1) |
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234 | (32) |
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266 | (25) |
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291 | (22) |
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6 Static Magnetic Field in Presence of Matter |
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313 | (106) |
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313 | (1) |
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6.2 Magnetic Current Densities |
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314 | (1) |
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315 | (2) |
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6.4 The Ampere Law of the Magnetic Field H |
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317 | (1) |
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6.5 Basic Kinds of Magnetic Materials |
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318 | (1) |
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6.6 Description of the Magnetization Curve |
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319 | (4) |
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6.7 Magnetic Circuits and Electromagnets |
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323 | (3) |
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6.8 Operating Straight Line and Operating Point |
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326 | (2) |
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328 | (2) |
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6.10 The Demagnetizing Field |
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330 | (89) |
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332 | (1) |
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332 | (18) |
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350 | (26) |
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376 | (43) |
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7 Methods for Solving Electrostatic and Magnetostatic Problems |
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419 | (92) |
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419 | (3) |
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7.2 The Method of Separation of Variables |
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422 | (3) |
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7.3 Green's Function Method |
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425 | (3) |
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428 | (3) |
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7.5 Application of Complex Analysis to Electromagnetism |
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431 | (10) |
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7.5.1 Transforming Boundary Conditions |
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432 | (1) |
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433 | (1) |
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7.5.3 Some Conformal Transformations |
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434 | (2) |
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436 | (5) |
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441 | (70) |
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7.6.1 The Finite Difference Method |
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441 | (4) |
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7.6.2 Other Important Techniques |
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445 | (3) |
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448 | (1) |
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448 | (63) |
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8 Electromagnetic Induction |
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511 | (56) |
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511 | (1) |
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512 | (3) |
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8.3 Motional Electromotive Force |
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515 | (3) |
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8.4 The General Law of Electromagnetic Induction |
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518 | (1) |
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8.5 Self-inductance and Mutual Inductance |
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519 | (4) |
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519 | (1) |
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520 | (3) |
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8.6 Voltage Between Two Points |
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523 | (44) |
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524 | (1) |
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524 | (9) |
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533 | (17) |
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550 | (17) |
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9 Energy of the Electromagnetic Field |
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567 | (32) |
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9.1 The Electrostatic Energy of Charges |
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567 | (1) |
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9.2 The Energy of a Capacitor |
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568 | (1) |
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9.3 The Electrostatic Energy of Distributed Charges |
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569 | (1) |
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9.4 Relationship Between Force and Electrostatic Energy |
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569 | (1) |
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9.5 Magnetostatic Energy of Quasi-stationary Currents |
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570 | (1) |
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571 | (1) |
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9.7 Magnetic Energy in a Hysteresis Loop |
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572 | (27) |
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573 | (1) |
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573 | (5) |
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578 | (6) |
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584 | (15) |
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599 | (28) |
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10.1 Generalization of Ampere's Law |
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599 | (1) |
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10.2 Maxwell's Equations for a Point |
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600 | (1) |
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10.3 Maxwell's Equations for a Domain |
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600 | (1) |
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601 | (1) |
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10.5 Surface of Discontinuity |
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602 | (25) |
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604 | (1) |
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604 | (10) |
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614 | (4) |
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618 | (9) |
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11 Motion of Charged Particles in Electromagnetic Fields |
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627 | (40) |
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627 | (1) |
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11.2 Trajectory of a Charge in a Homogeneous Electric Field |
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628 | (1) |
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11.3 Trajectory of a Charge in a Homogeneous Magnetic Field |
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629 | (2) |
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631 | (1) |
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11.5 Trajectory of a Charge in Simultaneous, Homogeneous and Constant, Magnetic and Electric Fields |
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632 | (1) |
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11.6 The Mass Spectrometer |
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633 | (1) |
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634 | (1) |
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635 | (1) |
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11.9 Relativistic Correction |
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636 | (1) |
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11.10 A Relativistic Particle in an Electromagnetic Field |
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637 | (1) |
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11.11 Charge in a Homogeneous Electric Field |
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637 | (3) |
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11.12 Charge in a Homogeneous Magnetic Field |
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640 | (27) |
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641 | (1) |
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641 | (11) |
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652 | (7) |
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659 | (8) |
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667 | (48) |
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12.1 Electromagnetic Wave Propagation: Wave Equation |
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667 | (1) |
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12.2 Plane and Spherical Waves |
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668 | (2) |
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12.3 Harmonic Plane Waves in Unbounded Dielectrics |
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670 | (2) |
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672 | (2) |
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12.5 Intensity and Poynting Vector |
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674 | (2) |
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12.6 Introduction to Fourier Analysis |
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676 | (39) |
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677 | (1) |
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677 | (8) |
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685 | (14) |
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699 | (16) |
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13 Reflection and Refraction |
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715 | (34) |
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13.1 Laws of Reflection and Refraction |
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715 | (1) |
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13.2 The Fresnel Coefficients |
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716 | (2) |
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13.3 Reflected and Transmitted Energy |
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718 | (31) |
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719 | (1) |
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719 | (11) |
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730 | (10) |
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740 | (9) |
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14 Wave Propagation in Anisotropic Media |
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749 | (38) |
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14.1 Concept of Anisotropy |
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749 | (2) |
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14.2 Susceptibility and Permittivity Tensors Definition |
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751 | (2) |
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14.3 Maxwell's Equations in an Anisotropic Linear Medium Free of Charges and Currents |
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753 | (2) |
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14.4 Electromagnetic Waves in Uniaxial Dielectrics |
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755 | (4) |
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14.5 Propagation of the Energy |
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759 | (2) |
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14.6 Geometrical Interpretation |
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761 | (1) |
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14.7 Electromagnetic Waves in Biaxial Crystals |
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762 | (2) |
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14.8 Crystal Classification |
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764 | (2) |
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766 | (21) |
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767 | (1) |
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767 | (4) |
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771 | (7) |
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778 | (9) |
Appendix A Matlab Programs |
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787 | (4) |
Appendix B Electric and Magnetic Properties of Several Materials |
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791 | (4) |
Bibliography |
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795 | (4) |
Index |
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799 | |