Evidence for undamped waves on ohmic materials - Roberto Batista Sardenberg (2015)
We present in this work a yet unexploited property of the Maxwell equations when applied to conductors. It was found that the real part impedance of passive circuits can achieve negative values. We have performed calculations which forecast this so far unobserved part of the impedance spectrum of conducting materials. A series of experiments which confirms our predictions was also conducted. The impedance of single spires and also of some coils of specific geometry were measured in the MHz frequency range. Metallic and carbon wires were used in constructing these spires and coils. Spectral analyses of our data demonstrate that in fact, the impedance of these passive circuits presents a frequency-dependent phase angle able to cover the full trigonometric cycle [-π, π]. Besides direct impedance readings, additional experiments were performed in order to check our data against possible systematic errors. We have constructed and enclosed our circuits within several kinds of electromagnetic shields, all of them presenting wall thickness several times larger than the skin dept of the radiation in the frequency range of measurement. With this, we guaranteed that external sources could not possibly induce any relevant noise in our measurements. The negative real part impedance effects were also present on these shielded experiments. In addition to that, it was confirmed on an oscilloscope screen that the voltage and current on a passive circuit may, in fact, present a phase difference of π. A first-principles theoretical model that assumes the presence of longitudinal undamped waves propagating in the system was devised. An expression for the impedance of circuits possessing theses waves was then obtained. This way we were able to make numerical calculations and predict the negative real part impedance effects. Experimental evidence for the existence of these longitudinal waves was also obtained. On these footings we have pointed out a special propagation mode of the electromagnetic field as the cause of the unusual observed spectral response. A discussion on the validity of impedance data and causality issues is also presented.