Experimentally is confirmed that helically coiled carbon nanotube (HCCNT) could be used as a small solenoid for generating spatially localized magnetic field. Current distribution during diffusive electronic transport likewise the inductivity of this quantum conductor depends on electric field. Despite slightly lower electron mobility in HCCNTs than that of the straight single wall carbon nanotubes, the coiled nanotubes are attractive for application as nonlinear nano-solenoids. Nonequilibrium electron distribution functions obtained by solving Boltzmann transport equation are used to predict average helical radius of current flow as a function of electric field intensity. Change of spatial distribution of electronic flow with applied electric field is considered and nonlinear inductivity of HCCNT is predicted.