The electrodeless plasma discharge is typically driven by radio frequency (RF) power supply within the range (0.2 &iexcl / 40 MHz). The applied power is coupled into the plasma inductively called inductively coupled plasma (ICP). RF ICP technique has achieved significance importance in a diversity of research and industrial applications for over the last threes decades. It is still required to undertake both theoretical and experimental research. In this work, RF ICP technique is applied on the torch modeling in 2D. Based on extended electromagnetic vector potential representation, an axisymmetric model in 2D is proposed for the calculations of the electromagnetic fields in an RF ICP torch. The influence of axial vector potential is included to the vector potential formulations. This is achieved by imposing a helical current carrying wire configuration. The corresponding governing equations are solved numerically by applying finite element method (FEM) using commercial partial differential equation solver (Flex PDE3). Based on this model, the plasma behavior and properties are examined in terms of plasma parameters. Besides, a comparative iii analysis is made between proposed model called helical configuration and the one currently available in the literature called circular configuration. This study shows relatively little difference between temperature fields predicted by two models. However, significant difference is observed between corresponding flows and electromagnetic fields. Especially, tangential flow which is observed in helical configuration vanishes in circular configuration. The proposed model offers an effective means of accounting for the variations of the helical coil geometry on the flow and temperature fields and achieving a better representation of the electromagnetic fields in the discharge. Finally, it is concluded that minimum number of turns (n = 2) yields significant difference between two models whereas, maximum allowable number of turns yield no distinctions on the results of two models in terms of azimuthally applied current. However, axial effect of current still exists but very small with respect to the result obtained with minimum number of turns.