A method is presented which allows to obtain the position-dependent electric field and charge density by fits to velocity profiles from edge-TCT data from silicon strip-detectors. The validity and the limitations of the method are investigated by simulations of non-irradiated $n^+p$ pad sensors and by the analysis of edge-TCT data from non-irradiated $n^+p$ strip-detectors. The method is then used to determine the position dependent electric field and charge density in $n^+p$ strip detectors irradiated by reactor neutrons to fluences between 1 and $10 times 10^{15}$ cm$^{-2}$ for forward-bias voltages between 25 V and up to 550 V and for reverse-bias voltages between 50 V and 800 V. In all cases the velocity profiles are well described. The electric fields and charge densities determined provide quantitative insights into the effects of radiation damage for silicon sensors by reactor neutrons.
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