ABSTRACT
This chapter discusses numerical solutions for electric and magnetic fields with time variations. It reviews the physical implications of the Maxwell equations in integral and differential forms. The chapter also reviews harmonic functions in complex exponential notation. It discusses equations for electric fields created by electrodes with harmonic voltages in imperfect dielectrics. The relationships hold at low to moderate frequencies. Resistive materials carry both displacement and conductive current. The chapter covers methods to solve for the potential with finite-element techniques and to interpret the results. It discusses the mathematical description of magnetic fields generated by harmonic applied currents in the presence of materials that may have both ferromagnetic and resistive properties. In this case, the electric fields associated with time-varying magnetic flux drive eddy currents. These current components may significantly affect the design of transformers, pulsed magnets, and magnetic recording devices.
