DC Internal Inductance for a Conductor of Rectangular Cross Section

In this paper, the dc internal inductance for conductors with rectangular cross section is investigated. Using a quasistatic Green's function, the magnetic fields inside a rectangular conductor are derived. These magnetic field expressions are used to formulate the internal inductance of the conductor. We present numerical results and closed-form expressions for the dc internal inductance for this geometry. Comparisons to various expressions found in the literature are made, and the inaccuracies of these other results are presented and discussed. Finally, we discuss some of the subtleties associated with the inductance of a single current path, in which we examine why the total and external inductances of a single infinitely long conductor have no physical meaning, whereas the internal inductance does.