Electromagnetic Fields in Conductive Media

The physics of electric and magnetic fields in matter is summarized by Maxwell's equations. This set of coupled, linear equations has source terms given by the charge density p and the current density J. Additional contributions arise from the time derivatives of the fields. In matter the macroscopic fields obey (Jackson 1975)

where E is called the electric field, and H is called the magnetic field3. The electric displacement D is related to the electric field E through e the dielectric constant: D = eE. The magnetic induction B is related to the electric field H through ¡i the magnetic susceptibility: B = ¡H.

3 Here Maxwell's equations are expressed in MKS units. The equations appear different from those in CGS units (Jackson 1975), but MKS is the more common in bioelectromagnetism (Gulrajani 1998).

Maxwell's equations reflect the basic principle of charge conservation. Taking the divergence of (3.4) and the time derivative of (3.1) leads to

Integrating over a closed volume V bounded by a surface S and using the divergence theorem (Arfken 1995) shows that the component of the current flowing outward across S equals minus the time rate of change of the charge in the volume bounded by S.

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