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Rosser G. Interpretation of classical electromagnetism
Rosser G.  Interpretation of classical electromagnetism







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: Interpretation of classical electromagnetism

: Rosser G.

:

This book presents Maxwell's equations and the laws of classical electromagnetism starting from the equations for the electric and magnetic fields due to an accelerating classical point charge. A microscopic perspective is used to interpret the electric field due to a current element, the origin of induced electromagnetic fields and detached electric field lines, motional electromagnetic fields, the mode of action of inductors and capacitors in AC circuits, conduction current flow, the Biot-Savart law, etc. A review of energy methods is presented in a way consistent with this microscopic approach, leading up to discussions of the conservation laws for a system of spatially separated moving charges and the Poynting vector hypothesis. After extending Maxwell's equations to field points inside dielectrics and magnetic materials, a brief review of special relativity is given stressing those topics that illustrate the essential unity of classical electromagnetism and special relativity.


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: 1997

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: 24.11.2013

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Absolute permeability      see Magnetic constant
Absolute permittivity      see Electric constant
AC theory      227258
AC theory, complex number method      258
Accelerating charge, discussion of fields      100
Accelerating charge, electric field      9294 406413
Accelerating charge, example of electric field      103 104
Accelerating charge, Li$\acute{e}$nard Wiechert potentials      9092
Accelerating charge, magnetic field      9294 406413
Accelerating charge, radiation fields      105107
Aether      156158
Amp$\grave{e}$re, definition of      24
Amp$\grave{e}$res circuital theorem      3335 37 43 138
Amp$\grave{e}$res formula for the forces between current elements      23
Amperian model for magnetic materials      338 341344 348
Amperian model for magnetic materials, electron spin      338 344
Angular momentum, conservation of in classical electromagnetism      314 315 320325
Angular momentum, definition of in classical electromagnetism      315
Antenna, dipole      71 72
Antenna, loop      72
Antenna, Yagi      72
Back emf      243 248
Barkhausen effect      339
Biot Savart approximation      100 130
Biot Savart law      24 28 29 33 35 42 44 143 211218 233 344 358
Biot Savart law, circuit      28
Biot Savart law, current distribution      29 33
Biot Savart law, deviations from differential form of      212218 392394
Biot Savart law, magnetostatics      28 33 392394
Bohm Ahranov effect      156
Boltzmann distribution      339
Bose particles      164
Bose Einstein statistics      163
Capacitor, charging      142145
Capacitor, CR circuit      249251
Capacitor, how it acts in an AC circuit      249251
Capacitor, reactance      251
Capacitor, voltage across      256
Cartesian coordinates      386 387
Causality in classical electromagnetism      373375
Cavendish, H.      3
Charge density      51 52 55
Charge density, macroscopic definition      51
Charge density, relativistic transformation      379381
Charge moving with uniform velocity, change of electric flux when crossing a surface      132 133
Charge moving with uniform velocity, electric field      9599
Charge moving with uniform velocity, electric flux from      130133
Charge moving with uniform velocity, magnetic field      9799
Charge, constancy of      6 7 359361 370 379 383
Charge, present position of      96
Conduction current flow      1621
Conduction current flow, charge distributions associated with      see Surface and boundary charge distributions
Conduction current flow, electric field inside conductors      20 21 395398
Conduction current flow, models of      18 19 402405
Conduction current flow, what sustains conduction currents      395398
Conductivity, electrical      18 349
Conductivity, use in derivation of Kirchhoffs second law      232
Conservation of angular momentum in classical electromagnetism      315
Conservation of angular momentum in classical electromagnetism, examples of      320324
Conservation of energy, classical electromagnetism      312314
Conservation of energy, electrostatics      16 313 314
Conservation of energy, Newtonian mechanics      267
Conservation of linear momentum, classical electromagnetism      304
Conservation of linear momentum, critique of      308
Conservation of linear momentum, example of two moving charges      305307
Conservation of linear momentum, Newtonian mechanics      267269
Conservative field      13
Continuity of charge and current densities      21 43
Continuity of charge and current densities, displacement current      43 145149
Continuity of charge and current densities, steady conditions      21
Continuity of charge and current densities, varying conditions      21
Coulomb gauge      8488 146
Coulomb, C. - A. de      3
Coulombs law      2 8 10 16 38 44 61 97 175177 332 368 369373
Counting of moving charges      167169
CR circuit      249251
Crab Nebula      201
Curl of a vector      386
Current density $\textbf{J}$, definition of      17 52 55
Current density $\textbf{J}$, relativistic transformation of      379381
Current element, force on in a magnetic field      2528
Current element, general formula for magnetic field      210
Current element, induction electric field due to      169177
Current element, magnetic field due to steady      206210
Current element, radiation electric field      193197
Current element, radiation magnetic field      209
Current element, total electric field      197 198
Currents, forces between using special relativity      367369
Cylindrical coordinates      389
DEL      385
Detached electric field lines      191 192
Diamagnetism      338
Dielectric, polarized, electric field of      329332
Dielectric, polarized, Gauss flux law      337
Dielectric, polarized, macroscopic field of      333
Dielectric, polarized, microscopic field of      332
Dielectric, polarized, surface charge distribution      329336
Dielectric, polarized, volume charge distribution      329336
Diracs relativistic wave equation      338
Displacement current      57 86 126128
Displacement current, charge moving with uniform velocity      126128
Displacement current, continuity of charge and current densities      147 148
Displacement current, discussion of      146
Displacement current, interpretation of      126128
Displacement current, low velocity limit      128 129
Displacement current, material medium      43 348 349
Displacement current, Maxwells equations      414418
Displacement current, system of moving charges      129
Displacement vector $\textbf{D}$      337 347 349
Divergence of a vector      386
Drift velocity      18
dAlembertian      46 58 146 150
dAlemberts equation      59
Einstein, A.      159 355 356 361 362
Elastic waves, longitudinal      156
Elastic waves, transverse      156
Electric circuits, electric fields due to      166205
Electric constant      4
Electric dipole, atomic dipoles      328
Electric dipole, electric field of      329
Electric dipole, moment of      329
Electric dipole, oscillating      see Oscillating electric dipole
Electric displacement $\textbf{D}$      337 349
Electric displacement $\textbf{D}$, oscillating magnetic dipole      196
Electric displacement $\textbf{D}$, radiation      69 70 160 193197
Electric displacement $\textbf{D}$, relativistic transformation of      378 379
Electric displacement $\textbf{D}$, relativistic transformations of      382
Electric displacement $\textbf{D}$, units      7
Electric displacement $\textbf{D}$, varying current distribution      201203
Electric displacement $\textbf{D}$, varying current in a circuit      180184
Electric field $\textbf{E}$, accelerating charge      9294 406413
Electric field $\textbf{E}$, charge moving with uniform velocity      9599
Electric field $\textbf{E}$, current element      170177 193195 197 198 202 203
Electric field $\textbf{E}$, definition      6
Electric field $\textbf{E}$, differential equation for      46
Electric field $\textbf{E}$, due to a steady current      177180
Electric field $\textbf{E}$, due to electric circuits      166205
Electric field $\textbf{E}$, electrostatics      47
Electric field $\textbf{E}$, induction      see Induction electric field
Electric field $\textbf{E}$, intensity of      1
Electric field $\textbf{E}$, Jefimenkos formula for      49 203205
Electric field $\textbf{E}$, macroscopic definition      52
Electric field $\textbf{E}$, oscillating electric dipole      6769
Electric field lines      112 162
Electric field lines, detached      191 192
Electric pressure      277
Electric tension      277
Electromagnetic energy density      317
Electromagnetic field, rate of doing work      285 286
Electromagnetic induction      117126
Electromagnetic induction, accelerating charge      122
Electromagnetic induction, charge moving with uniform velocity      117119
Electromagnetic induction, introduction      4042
Electromagnetic induction, low velocity limit      128 129
Electromagnetic induction, motional (dynamo) emf      40 259266
Electromagnetic induction, system of charges      123 129
Electromagnetic induction, transformer emf      4042 228230 244-246
Electromagnetic induction, vector potential      125
Electromagnetic momentum      see Potential (electromagnetic) momentum
Electromagnetic waves, empty space      47
Electromagnetic waves, linear homogenous medium      350 351
Electromagnetic waves, oscillating electric dipole      69 70
Electromagnetic waves, Poynting vector      294297
Electromagnetic waves, propagation in a dielectric      352 353
Electromagnetic waves, radiation pressure      301303
Emf, motional      40 259266
Emf, transformer      4042 228230 244-246
Emf, Van de Graaff      20 395398
Energy density of the electromagnetic field      284 317
Energy, conservation      see Conservation of energy
Energy, electric      282 283
Energy, electromagnetic field      282285 312 313
Energy, flow of in DC circuits      405
Energy, magnetic      283
Faller, J. E.      3
Faraday disk generator      262
Faraday, M.      157
Faradays law of electromagnetic induction      41 42 44 57 119121 124126 158 188 189 232234 243 338 348
Faradays law of electromagnetic induction, critique of      124126
ferromagnetism      339
Fresnel, A. - J.      156
Fresnels equations      352
Galilean reference frame      357
Galilean transformations      159 263 355 359
Gauge transformation      84 85
Gauss flux law, accelerating charge      112
Gauss flux law, charge distribution      10 37
Gauss flux law, charge moving with uniform velocity      110114
Gauss flux law, dielectrics      337
Gauss flux law, electric field lines      9 112
Gauss mathematical theorem      387 388
Gradient of a scalar      385
Grassmanns equation      22 23
Hall effect      2628 263
Hamiltonian      154
Hamiltons equations      153 154
Hertz vector      88
Hill, H. A.      3
Induction electric field, circular coil      186189
Induction electric field, current element      169177
Induction electric field, related to the projected position      174177
Induction electric field, solenoid      189191
Induction electric field, transformer      228230
Induction electric field, varying current      180184
Induction electric field, what a voltmeter measures      236 237
Inertial observer      357
Inertial reference frame      357
Information collecting sphere      62 73 9092 167 169172 174 175 177
Jefimenkos equations      48 49 82 83 203205 221
Joule heat      19 20 284 290 319
Kelvin, Lord      157 158 161
Kirchhoffs laws, first law      227 238 240 257 319
Kirchhoffs laws, second law      232 238 240 252 253 257 258 319
Lagranges equations      153 154
Lagrangian      153 154
Laplaces equation      13 16
Laplacian      46 58 146 150 386 387 389
Lawton, W. - E.      3
LCR circuit      161 246 247 251 252 285
LCR circuit, energy method      285
LCR circuit, voltage across elements      253257
Length contraction      366 367 369 380
Lenzs law      121 235 243 262
Li$\acute{e}$nard Wiechert potentials      9092 94 100 108 128 169 223 406413
Light velocity      48 159 358 419
Light velocity, constancy of      358 359
Light velocity, material medium      351
Light velocity, relation to $\epsilon_0$and $\mu_0$      44 48 358
Line of charge, moving      134138
Lorentz condition      57 58 84 153 155
Lorentz condition, applied to oscillating electric dipole      73 84
Lorentz force law      1 24 151154 158 261 267 269 304306 321325 370 373-376
Lorentz force law, motional emf      261
Lorentz gauge      1 58 59 84 88 153
Lorentz transformations      159 356 362365 419
Lorentz, H. A.      2 11 49 50
LR circuit      247 248 283 284
Macroscopic field variables, definition of      5052 390
Macroscopic field variables, differentiation of      53 390
Magnetic constant      24
Magnetic dipole, Amperian model      338 341344
Magnetic dipole, definition      338
Magnetic dipole, magnetic field      188
Magnetic dipole, oscillating      221 222
Magnetic dipole, vector potential      340344
Magnetic field $\textbf{B}$      1 24 25
Magnetic field $\textbf{B}$, accelerating charge      9294 406413
Magnetic field $\textbf{B}$, charge moving with uniform velocity      9599
Magnetic field $\textbf{B}$, current element      206210
Magnetic field $\textbf{B}$, differential equation for      45
Magnetic field $\textbf{B}$, divergence of      30
Magnetic field $\textbf{B}$, Jefimenkos equation for      48 221
Magnetic field $\textbf{B}$, macroscopic definition      52
Magnetic field $\textbf{B}$, magnetostatics      2224
Magnetic field $\textbf{B}$, Maxwell stress tensor      270275 297299
Magnetic field $\textbf{B}$, oscillating electric dipole      65 66 219
Magnetic field $\textbf{B}$, oscillating magnetic dipole      221 222
Magnetic field $\textbf{B}$, radiation      69 70
Magnetic field $\textbf{B}$, relativistic transformation of      378 379
Magnetic field $\textbf{B}$, solenoid      230
Magnetic field $\textbf{B}$, varying current distribution      220 221
Magnetic field $\textbf{B}$, vector potential      32 56
Magnetic field intensity $\textbf{H}$      344 345 347
Magnetic field intensity $\textbf{H}$, relativistic transformation of      382
Magnetic field lines      25 31 115 162
Magnetic flux density $\textbf{B}$      see Magnetic field
Magnetic forces as a second order effect      3640 367369
Magnetic induction $\textbf{B}$      see Magnetic field
Magnetic materials, Amperian model      338
Magnetic materials, macroscopic field due to      340 341
Magnetic materials, microscopic field in      340 341
Magnetic materials, surface current distributions      341344
Magnetic materials, volume current distributions      341344
Magnetic monopole      31 139
Magnetic pressure      272 274
Magnetic tension      274
Magnetization current density      347 349
Magnetization vector $\textbf{M}$      327 339 340
Maxwell stress tensor      269282
Maxwell stress tensor, electric fields      276 277
Maxwell stress tensor, electrostatic example      278280
Maxwell stress tensor, general case      277 278 299
Maxwell stress tensor, magnetic fields      270275
Maxwell stress tensor, magnetostatic example      280 281
Maxwell stress tensor, matrix form      275
Maxwell stress tensor, radiation pressure      301303
Maxwell stress tensor, tensor form      275 277 278
Maxwell stress tensor, varying conditions      297301
Maxwell Lorentz equations      2 49 50 62 142 327 332
Maxwell, J. C.      3 43 46 47 86 87 157 158 161
Maxwells equations      1 2 11 16 18 22 4446 48 49 55 108165
Maxwells equations, charging capacitor      142145
Maxwells equations, comparison with the use of the potentials $\phi$ and $\textbf{A}$      153156
Maxwells equations, curl of $\textbf{B}$      3335 42 43 79 80 126130 141 155 414-418
Maxwells equations, discussion of Maxwells equations      149153
Maxwells equations, displacement current      42 43 126128 414418
Maxwells equations, divergence of $\textbf{B}$      30 77 114 115
Maxwells equations, macroscopic fields      5054 327 328 353 354
Maxwells equations, magnetic dielectrics      346349
Maxwells equations, material medium      5053 348350
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