A simple Rankine-like vortex model of the dust devil behaving as a magnetic solenoid has been constructed. It is augmented with a one-dimensional model describing steady vertical distribution of the electric charge in the dust devil. For terrestrial dust devils, the model permits uniform vertical distribution of the negatively charged dust within the main vortex flow. For higher electric conductivity of air on Mars, the model hints on a rapid decay with altitude of the dust electrification, with e-folding height order of several tens of meters, which is much less than the total dust column height. It is shown that some characteristic features of recently discovered ULF magnetic emission from the terrestrial dust devil can be interpreted in terms of interaction between negatively charged smaller-scale vortex filaments inside the main vortex. It is conjectured that such ULF magnetic emission should be accompanied by the emission of sound waves of approximately doubled frequency.