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phys documents (dragged) 17

# phys documents (dragged) 17 - 10 Physics Formulary by ir...

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Unformatted text preview: 10 Physics Formulary by ir. J.C.A. Wevers Here, the freedom remains to apply a gauge transformation . The Felds can be derived from the potentials as follows: E =-∇ V- ∂ A ∂ t , B = ∇ × A ¡urther holds the relation: c 2 B = v × E . 2.3 Gauge transformations The potentials of the electromagnetic Felds transform as follows when a gauge transformation is applied: A = A- ∇ f V = V + ∂ f ∂ t so the Felds E and B do not change. This results in a canonical transformation of the Hamiltonian. ¡urther, the freedom remains to apply a limiting condition. Two common choices are: 1. Lorentz-gauge: ∇ · A + 1 c 2 ∂ V ∂ t = 0 . This separates the differential equations for A and V : V =- ρ ε , A =- μ J . 2. Coulomb gauge: ∇ · A = 0 . If ρ = 0 and J = 0 holds V = 0 and follows A from A = 0 . 2.4 Energy of the electromagnetic Feld The energy density of the electromagnetic Feld is: dW d Vol = w = HdB + EdD The energy density can be expressed in the potentials and currents as follows:...
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