On the statement of the stationary electric field problem

The equations commonly used for the de(t)ermination of a stationary electri c field E incorrectly des(c)ribe this field in the region V-ex containing e xtrinsic currents j(ex). Equations correctly determining the field E everyw here, including the region Vex, are derived from the Maxwell equations and have the form rot E = rot E-ex, div sigmaE = -div sigmaE(exp), where E-exp is the potential part of the extrinsic field E-ex. This is achieved through a redistribution of sources between the first and second Maxwell equations . The stationary electric field is no longer potential everywhere in space and is exited outside the region V-ex by the eddy part of the extrinsic cur rent. The meaning of the term "extrinsic field E-ex" as well as the relatio n j(ex) = sigmaE(ex), is refined. Using the stationary electric field as an example. I show that the Maxwell equations must be written in the form rot H = sigma E j(e), rot E = i omega muH - j(m), where j(e) = sigma E-exp, j( m) = -rot E-ex, and sigma = sigma - i omegae is the complex electric conduc tivity of the medium.