Maxwell's Equations - "Microscopic" Vs "Macroscopic" Formulations of The Maxwell Equations

"Microscopic" Vs "Macroscopic" Formulations of The Maxwell Equations

The microscopic variant of Maxwell's equation expresses the electric E field and the magnetic B field in terms of the total charge and total current present including the charges and currents at the atomic level. It is sometimes called the general form of Maxwell's equations or "Maxwell's equations in a vacuum". The macroscopic variant of Maxwell's equation is equally general, however, the difference being one of book keeping.

"Maxwell's macroscopic equations", also known as Maxwell's equations in matter, are more similar to those that Maxwell introduced himself. Unlike the "microscopic" equations, they factor out the bound charge and current to obtain equations that depend only on the free charges and currents. The cost of this factorization is that additional fields, the displacement field D and the magnetizing field-H, are defined that need to be determined. Phenomenological constituent equations relate the additional fields to the electric field E and the magnetic B-field, often through a simple linear relation.

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