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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 =- , A =- J . 2. Coulomb gauge: A = 0 . If = 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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This note was uploaded on 01/30/2011 for the course PHYSICS 208 taught by Professor Ye during the Spring '10 term at Blinn College.

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