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Published byZoe Salazar Modified over 4 years ago

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1 ECE Field Equations – Vector Form Material Equations Dielectric Displacement Magnetic Induction

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2 Field-Potential Relations I Potentials and Spin Connections A: Vector potential Φ: scalar potential ω e : Vector spin connection of electric potential ω m : Vector spin connection of magnetic potential ω 0 : Scalar spin connection (electric)

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3 ECE Field Equations in Terms of Potential I

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4 ECE Field Equations in Terms of Potential with cold currents I ρ e0, J e0 : normal charge density and current ρ e1, J e1 : cold charge density and current

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5 Antisymmetry Conditions of ECE Field Equations I All these relations appear in addition to the ECE field equations and are contained in them. They replace Lorenz Gauge invariance and can be used to derive special properties.

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6 Field-Potential Relations II Potentials and Spin Connections A: Vector potential Φ: scalar potential ω E : Vector spin connection of electric field ω B : Vector spin connection of magnetic field or

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7 ECE Field Equations in Terms of Potential II Version 1

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8 ECE Field Equations in Terms of Potential II Version 2

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9 ECE Field Equations in Terms of Potential with cold currents II, Version 1 ρ e0, J e0 : normal charge density and current ρ e1, J e1 : cold charge density and current

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10 Antisymmetry Conditions of ECE Field Equations II

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Field of uniformly moving charge LL2 Section 38. Origins are the same at t = 0. Coordinates of the charge e K: (Vt, 0, 0) K’: (0, 0, 0)

Field of uniformly moving charge LL2 Section 38. Origins are the same at t = 0. Coordinates of the charge e K: (Vt, 0, 0) K’: (0, 0, 0)

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