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The Electromagnetic Field |
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1 | (46) |
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A Presentation of An Electromagnetic Field |
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2 | (1) |
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Definitions of the fields E and B |
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2 | (1) |
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Field Sources: Charge and Currents |
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3 | (9) |
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Microscopic and macroscopic theory |
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4 | (1) |
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Charge and current densities |
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4 | (2) |
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6 | (1) |
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Singular source densities |
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6 | (1) |
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Surface charge density and surface current density |
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7 | (1) |
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Densities of a line charge and line current |
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8 | (1) |
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9 | (1) |
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Discontinuities in a field |
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10 | (1) |
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Field discontinuities caused by the surface density of a scalar source |
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10 | (1) |
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Field Discontinuities caused by the surface density of a vector source |
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11 | (1) |
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Maxwell's Equations in a Vacuum |
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12 | (6) |
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Maxwell's equations in differential form |
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15 | (1) |
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Maxwell's equations in integral form |
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16 | (2) |
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An electromagnetic field in materials |
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18 | (21) |
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A macroscopic model of a conductive material |
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19 | (1) |
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Density of a conductive current in a material. Ohm's law |
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19 | (1) |
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A conductor in an electric field |
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20 | (2) |
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Polarization of materials. The vector of polarization P |
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22 | (2) |
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Dielectric in an electric field |
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24 | (2) |
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Magnetization of materials |
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26 | (2) |
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A model of amperian currents in a magnetic material |
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28 | (1) |
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A model of magnetic charge and current |
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29 | (2) |
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Field vectors D and H. Electric and magnetic fluxes |
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31 | (3) |
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Materials and constitutive relationships |
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34 | (1) |
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35 | (1) |
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35 | (1) |
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36 | (1) |
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36 | (1) |
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37 | (1) |
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38 | (1) |
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Maxwell's Equations for fields in a material |
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39 | (8) |
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Maxwell's equations for the model using amperian current |
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40 | (1) |
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40 | (1) |
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40 | (2) |
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Maxwell's equations for a model with magnetic charge |
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42 | (1) |
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42 | (1) |
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43 | (1) |
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Maxwell's equations for field vectors E, B, D and H |
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44 | (2) |
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46 | (1) |
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Electromagnetic potentials |
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47 | (26) |
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Vector and scalar potential functions |
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47 | (9) |
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Potentials and antipotentials in a dielectric without sources |
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47 | (1) |
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Vector and scalar potentials |
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48 | (1) |
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49 | (1) |
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50 | (1) |
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Potentials in a conductive source-free material |
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51 | (2) |
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Potentials and antipotentials of a given distribution of independent sources |
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53 | (1) |
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53 | (1) |
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54 | (1) |
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Static charge and currents |
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54 | (1) |
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Magnetic charge and currents |
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55 | (1) |
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56 | (5) |
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57 | (1) |
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57 | (1) |
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58 | (1) |
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59 | (1) |
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A field with independent sources |
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59 | (2) |
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61 | (3) |
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64 | (5) |
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The scalar potential of a point charge |
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65 | (1) |
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Potentials of a time dependent distribution of space charge in an unbounded space |
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66 | (2) |
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Retarded potentials in an unbounded space |
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68 | (1) |
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Wave Equations and Integrals of Potentials |
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69 | (4) |
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72 | (1) |
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Energy and Forces In an Electromagnetic Fields |
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73 | (28) |
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The Influence of an Electromagnetic Field on Moving Charges |
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73 | (3) |
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Forces on charges in motion |
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74 | (1) |
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Energy and power delivered to charges in motion |
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75 | (1) |
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76 | (7) |
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The conservation of electromagnetic energy. Poynting's theorem |
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77 | (1) |
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Poynting's theorem in differential form |
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77 | (1) |
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Poynting's theorem in an integral form |
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78 | (1) |
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Conservation of electromagnetic energy in a vacuum |
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78 | (2) |
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Stored electromagnetic energy in a cacuum |
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80 | (2) |
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The flow of electromagnetic energy. Poynting's vector |
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82 | (1) |
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A Material In An Electromagnetic Field |
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83 | (8) |
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Electromagnetic energy absorbed in a material |
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83 | (2) |
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Poynting's theorem in a material |
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85 | (1) |
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Energy of polarization and electric energy |
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86 | (3) |
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Energy of magnetization and magnetic energy |
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89 | (1) |
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Poynting's theorem and electric and magnetic energy in materials |
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90 | (1) |
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Volume Forces and Surface Stresses |
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91 | (10) |
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Surface stresses in free space |
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91 | (2) |
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93 | (1) |
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The vector of electromagnetic stress |
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94 | (2) |
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Forces and surface stresses in materials |
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96 | (1) |
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Surface stresses in static fields at the boundary between two materials |
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97 | (3) |
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100 | (1) |
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101 | (50) |
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Equations of a Static Electric Field |
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101 | (2) |
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Scalar electric potential |
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102 | (1) |
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Visual Presentation of a Static Electric Field |
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103 | (1) |
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Energy Stored in a Static Electric Field |
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104 | (3) |
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Energy-based determination of forces in a static electric field |
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106 | (1) |
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107 | (3) |
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Capacitance of a condenser |
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107 | (1) |
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A system of conductors and partial capacitances |
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108 | (2) |
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The Solution of Static Electric Fields |
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110 | (4) |
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The superposition of solutions of Poisson's Equation |
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111 | (1) |
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The uniqueness of solutions of Poisson's equation |
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111 | (2) |
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Integral of Poisson's equation and Green's functions |
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113 | (1) |
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The Solution of Laplaces's Equation by a separation of Variables |
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114 | (8) |
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Cartesian coordinate system |
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114 | (3) |
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Cylindrical coordinate system |
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117 | (3) |
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A spherical coordinate system |
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120 | (2) |
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A Given Distribution of Charge in an Unbounded Space |
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122 | (11) |
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122 | (4) |
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126 | (3) |
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129 | (2) |
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Volume charge and a multipole expansion |
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131 | (2) |
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Distribution of Charge in a Bounded Space and the Method of Images |
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133 | (18) |
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Green's functions of plane metal boundaries |
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133 | (1) |
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A point charge in front of a conductive plane |
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133 | (1) |
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A point charge in a conductive angle |
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134 | (1) |
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A line charge in front of a conductive plane |
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135 | (3) |
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Green's functions of a plane dielectric boundary |
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138 | (1) |
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A point charge in front of a plane boundary between dielectrics |
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138 | (3) |
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Green's functions of a cylindrical boundary |
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141 | (1) |
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A conductive cylindrical boundary |
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141 | (3) |
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A dielectric cylindrical boundary |
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144 | (2) |
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Green's function of a conductive spherical boundary |
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146 | (3) |
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149 | (2) |
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A Static Current Field in a Conductor |
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151 | (6) |
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The field of Charge in uniform motion |
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151 | (1) |
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Equations of a current Field and Field Analogies |
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152 | (2) |
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Solution of a Current Field by the Method of Images |
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154 | (3) |
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156 | (1) |
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157 | (26) |
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Equations of a Static Magnetic Field |
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157 | (1) |
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Potentials in a Static Magnetic Field |
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158 | (1) |
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Magnetic vector potential |
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158 | (1) |
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158 | (1) |
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A Visual Presentation of a Static Magnetic Field |
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159 | (1) |
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Energy stored in a Static Magnetic Field |
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160 | (2) |
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Energy-based determination of forces in a static magnetic field |
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161 | (1) |
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162 | (3) |
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163 | (1) |
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The inductances of a systems of current loops |
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164 | (1) |
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A magnetic Field in a Current-Free Region |
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165 | (5) |
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The Field of Given Currents in an Unbounded Space |
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170 | (10) |
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The field of line currents in an unbounded space |
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171 | (4) |
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The field of a surface current |
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175 | (2) |
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The field of volume currents and a multiple expansion |
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177 | (3) |
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Given Currents in a Bounded Space and the Method of Images |
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180 | (3) |
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182 | (1) |
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A Quasi-Static Electromagnetic Field |
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183 | (34) |
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Equations of a Quasi-Static Field |
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183 | (3) |
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Validity of a quasi-static approximation |
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185 | (1) |
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Field Equations in a Phasor Domain and Quasi-Static sinusoidal Fields |
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186 | (3) |
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Sinusoidal time dependent fields and phasor notation |
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186 | (1) |
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Electromagnetic Potentials in a phasor domain and a quasi-static approximation |
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187 | (2) |
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Energy in a Quasi-static Field |
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189 | (2) |
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Energy and power in a sinusoidal field |
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189 | (2) |
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The Solution of a Quasi-Static Field in Conductors |
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191 | (14) |
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Current Loops in a Quasi-Static Field |
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205 | (12) |
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Steady current loops in a quasi-static field |
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206 | (4) |
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Movement of a current loop in a quasi-static field electromagnetic induction |
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210 | (2) |
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Electromechanical energy conversion |
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212 | (4) |
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216 | (1) |
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217 | (92) |
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Wave Equations of a Field in an Unbounded Source-Free Space |
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217 | (3) |
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218 | (1) |
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A separation of variables of the wave equation |
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218 | (2) |
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A Plane Wave in an Unbounded Space |
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220 | (16) |
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The separation of the Helmholtz equation |
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220 | (1) |
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Equations of a plane wave |
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221 | (5) |
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Plane waves sinusoidal in time |
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226 | (4) |
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Plane waves sinusoidal in space |
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230 | (2) |
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Fundamental characteristics of sinusoidal plane waves |
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232 | (1) |
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232 | (1) |
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233 | (1) |
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234 | (2) |
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The Propagation of Plane Waves |
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236 | (19) |
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236 | (1) |
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237 | (5) |
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242 | (2) |
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Waves in a lossy conductive material |
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244 | (3) |
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Classification of materials into insulators and conductors |
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247 | (1) |
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248 | (2) |
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250 | (2) |
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252 | (3) |
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255 | (7) |
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Dispersion in dielectrics; the classical model for ε(ω) |
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256 | (2) |
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258 | (2) |
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The group velocity of a signal |
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260 | (2) |
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The Propagation of a Sinusoidal plane wave in Half-Bounded Regions |
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262 | (12) |
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Reflection and refraction at a plane boundary |
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263 | (1) |
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The laws of reflection and refraction |
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263 | (2) |
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Fresnel formulae and the influence of polarization |
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265 | (5) |
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The boundary between two dielectrics |
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270 | (1) |
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Transmission of a wave into a lossy material |
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271 | (3) |
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Propagation of Guided Plane Waves |
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274 | (23) |
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275 | (7) |
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A terminated transmission line |
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282 | (2) |
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284 | (6) |
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Modes in a rectangular waveguide |
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290 | (4) |
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294 | (3) |
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Electromagnetic Wave Radiation |
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297 | (12) |
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Electric Dipole radiation |
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297 | (6) |
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The radiation field of a linear conductor |
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303 | (5) |
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308 | (1) |
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The Finite Element Method |
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309 | (50) |
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309 | (5) |
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The integral form, and its approximation |
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311 | (1) |
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A functional us an integral form |
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311 | (1) |
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312 | (2) |
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Two-dimensional static fields |
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314 | (35) |
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An integral form equivalent to poisson's equation |
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314 | (2) |
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Application of FEM to the integral form equivalent to Poisson's equation |
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316 | (1) |
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An approximation of the geometry of the problem's domain |
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317 | (4) |
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Organization of data on subdivision into elements |
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321 | (1) |
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An approximation of the function on the element |
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322 | (3) |
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Element integral forms of linear triangular elements used in solving Poisson's equation |
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325 | (3) |
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Assembly of a system of equations |
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328 | (1) |
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The algorithm for the assembly of the system |
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329 | (1) |
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The solution of systems of linear algebraic equations in FEM |
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330 | (1) |
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330 | (1) |
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331 | (6) |
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Organization of data on the equation system |
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337 | (4) |
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Calculation of electric and magnetic field strength |
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341 | (1) |
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Calculation of the electric field vectors E and D |
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342 | (1) |
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Calculation of the magnetic field vectors B and H |
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343 | (1) |
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Visual representation of results of calculation by lines of constant potential |
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343 | (1) |
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Calculation of equipotential lines |
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344 | (1) |
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An example of calculation |
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345 | (4) |
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349 | (4) |
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353 | (6) |
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353 | (2) |
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355 | (3) |
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358 | (1) |
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359 | (30) |
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359 | (2) |
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Three-Dimensional Static electric Fields |
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361 | (4) |
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An integral formulation of the problem |
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361 | (1) |
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362 | (3) |
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Scattering of electromagnetic Waves |
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365 | (13) |
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Integral form of the equations |
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366 | (1) |
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366 | (2) |
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368 | (3) |
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Solution of a scattering problem by MOM |
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371 | (1) |
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371 | (4) |
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375 | (3) |
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378 | (11) |
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378 | (1) |
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The integral formulation of scattering problems involving thin wires |
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379 | (2) |
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Models of excitation for radiation sources |
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381 | (2) |
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The solution of Pocklington's equation by the application of MOM |
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383 | (3) |
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386 | (2) |
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388 | (1) |
| APPENDIX A: DIRACδ-FUNCTION |
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389 | (1) |
| APPENDIX B: VECTOR CALCULUS |
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390 | (4) |
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B.1 Vector multiplication |
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390 | (1) |
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B.2 Differential relationships |
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391 | (2) |
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B.3 Integral relationships |
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393 | (1) |
| APPENDIX C: COORDINATE SYSTEMS |
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394 | (4) |
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C.1 A Cartesian coordinate system |
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394 | (1) |
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C.2 A Cylindrical coordinate system |
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395 | (1) |
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C.3 A Spherical coordinate system |
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396 | (2) |
| APPENDIX D: BESSEL'S DIFFERENTIAL EQUATION |
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398 | (4) |
| APPENDIX E: EXPANSION OF FUNCTIONS INTO EXPONENTIAL SERIES |
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402 | (1) |
| APPENDIX F: ELLIPTIC INTEGRALS |
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403 | (2) |
| References |
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405 | (2) |
| Index |
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407 | |
