Advanced Electromagnetism Lecture 3 of 15

January 27, 2012 by M. Fabbrichesi

M. Fabbrichesi , SISSA

3. Maxwell's equations in macroscopic media

This lecture is dedicated to Maxwell's equations in macroscopic media. Currents and charges are splitted into two terms ("external" and "induced") e.g: J=Jext+Jind. This lead to a rewriting of Maxwell's equation in terms of a new set of fields: D,H,B,E that keep into account the electric and magnetic answers of materials to applied fields [Jackson, Introduction I.4]. Concept of polarization and magnetization are introduced. It is seen that macroscopic fields such as D can be expanded in series containing dipole, quadrupole....terms [Jackson, Eq. I.9]. Next, boundary conditions at interfaces between different media are obtained by applying Maxwell's equations for the set D,H,B,E [Jack. Eqs. I.17-18 and I.19-20]. Then electrostatics and magnetostatics law are considered for introducing auxiliary fields called scalar and vector potentials that will be later very helpful for a Lagrangian description of electromagnetism. Finally, concerning the "reality" of the vector potential, the Aharonov-Bohm effect is briefly mentioned.

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