DIFFUSION OF CURRENT INTO CONDUCTORS J.Edwards* and T.K Saha** * Research Concentration in Electrical Energy Queensland University of Technology ** Department of Computer Science and Electrical Engineering University of Queensland. Currents are established on the surface of conductors by the propagation of electromagnetic waves in the insulating material between them. If the load is less than the characteristic impedance of the insulating material of the line, multiple reflections and retransmissions eventually build up the line current to that required by the load. The currents are initially established on the surface of the conductors before diffusing relatively slowly into the interior and gives rise to the skin effect. The diffusion velocity depends the conductivity, permeability, thickness of the conductor, and the frequency of the excitation, and such effects of the diffusion process are difficult to conceptually appreciate. Fortunately, the diffusion of heat into solids is very similar, and will be used as an analogy to aid understanding. This diffusion is the means whereby current moves into conductors and flux into of magnetic cores. 1. INTRODUCTION Current flow in conductors is often associated with liquid flow in pipes, at least conceptually. The ‘liquid’ being the sea of free electrons, in the conduction band of the material, that drift along the conductor with a velocity that is proportional to the electric field and gives rise to the current, J = σ E. This liquid flow analogy is quite reasonable for steady dc currents, giving a conceptual understanding of Ohms law. However, while good conductors such as copper present little opposition to electrons moving at constant velocity, they strongly oppose electron accelerations, because the relatively large currents (J=σ E) produce magnetic fields that are much higher than those produced by displacement currents in free space. These high magnetic fields move at relatively low velocities since the back emfs induced by their motion cannot be any larger than the driving E field. These induced emfs generate eddy currents within the conductor, which also oppose the diffusion due to associated energy losses. These limited back emfs and eddy currents cause any changes in the surface electric field (current) to move very slowly into the interior of conductors and suffer significant. The relatively slow velocity of penetration depends on the conductivity, and permeability of the material. The higher the conductivity, permeability, and size of the conductor, the slower is diffusion velocity. For a very large copper conductor the penetration velocity at a frequency 50Hz is approximately 8 m/s. This relatively low velocity is not very apparent in every day applications because the currents needed to energise electrical loads initially propagate along the cable (transmission line) to the load as displacement currents in the insulation, at velocities approaching c. The displacement current builds up the line current on the surface of the conducting cables by multiple reflections, and this current diffuses into the interior of the conductor [1]. Thus current changes (electron accelerations) actually move into the conductors from the outside surfaces and only have to diffuse through the thickness of the conductors (half the diameter) rather than along the whole length of the cable from the power source to the load. If it were not for the displacement current setting up the surface currents in the first instance, energy transmission, (other than via relatively steady dc currents) via copper conductors would be virtually impossible because of the long diffusion times and attenuations. The skin effect results from the fact that at the particular frequency of operation the surface currents only have time to diffuse into the conductor to the skin depth in the ¼ period of the supply frequency. Surface currents move into the conductor on the rising part of the current waveform. Once the surface currents peak and start to fall, the interior currents move back out towards the surface of the conductor. At 50Hz the skin depth in copper is approx 10mm. The same diffusion process also applies to surface magnetic flux moving into the interior of magnetic cores, since most cores are electrically conductive. Surface flux changes produce a driving H field (∆H s = ∆B s / μ) that drives any change in surface flux into interior of the core. The changing flux levels induce back emfs as they move into the core, with resulting eddy currents, whose H fields oppose the driving H field. These induced H fields, due to changing surface