We investigate THz radiation absorption by charge carriers, focusing on the mobility in nanorods and wires. We show that for short rods the mobility is limited by the high spacing of the charge carrier energy levels, while for longer wires (greater 25 nm) finite dephasing results in considerably higher low frequency mobility. Analyzing the length, temperature and population dependence, we demonstrate that, apart from the temperature dependent dephasing, the mobility becomes strongly charge carrier population dependent. The latter results in no simple linear relationship between carrier density and conductivity. Additionally their thermal distribution determines the mobility, measured in experiments. We further show that Drude or Plasmon models apply only for long wires at elevated temperatures, while for short length quantization results in considerable alterations. In contrast to those phenomenological models, i.e. a negative imaginary part of the frequency-dependent conductivity in a nanosystem can be understood microscopically. Based on the results, we develop guidelines to analyze 1D terahertz conductivity spectra. Our approach provides also a new tool to optimize the mobility by nanowire length as well as to analyze the dephasing, not by conventional wave mixing techniques, but by coherent optical pump-THz probe spectroscopy.