The design model and key parameters of the material design for the control of induced magnetic flux at the near-field and efficient power transfer in a modified wireless power transfer (WPT) system with a large air gap of wireless electric vehicles were investigated through analytical simulations for magnetic vector and time-domain transient analysis. Higher saturation magnetic core with low core loss induced a stronger vertical magnetic field by the W-type primary coil in the WPT system with a gap of 20 cm at 20 kHz, which is shown from the vector potentials of the magnetic induction. The transient analysis shows that the higher magnetic fluxes through the pick-up cores lead to a linear increment of the alternating voltage with a sinusoidal waveform in the non-contact energy transfer system.