The generation of parallel electric fields by the propagation of ion cyclotron waves (with frequency 0.3 ωci) in the plasma with a transverse density inhomogeneity was studied. Using two-fluid, cold plasma linearised equations, it was shown for the first time that, in this particular context, E∥ generation can be understood by an analytic equation that couples E∥ to the transverse electric field of the driving ion cyclotron wave. It was proven that the minimal model required to reproduce the previous kinetic simulation results of E∥ generation [Tsiklauri et al 2005, Génot et al 2004] is the two-fluid, cold plasma approximation in the linear regime. By considering the numerical solutions it was also shown that the cause of E∥ generation is the electron and ion flow separation induced by the transverse density inhomogeneity. We also investigate how E∥ generation is affected by the mass ratio and found that amplitude attained by E∥ decreases linearly as inverse of the mass ratio mi/me. For realistic mass ratio of mi/me=1836, such empirical scaling law, within a time corresponding to 3 periods of the driving ion cyclotron wave, is producing E∥=14 Vm−1 for solar coronal parameters. Increase in mass ratio does not have any effect on final parallel (magnetic field aligned) speed attained by electrons. However, parallel ion velocity decreases linearly with inverse of the mass ratio mi/me. These results can be interpreted as following: (i) ion dynamics plays no role in the E∥ generation; (ii) E∥ ∝ 1/mi scaling is caused by the fact that ωd = 0.3 ωci ∝ 1/mi is decreasing with the increase of ion mass, and hence the electron fluid can effectively “short-circuit” (recombine with) the slowly oscillating ions, hence producing smaller E∥.