## 3 Models and Methods
### Exposure Scenarios  
SAE J2954 [16] recommends three standard power levels: WPT1 at 3.7 kW, WPT2 at 7.7 kW, and WPT3 at 11 kW. In this study, the WPT system integrated into the vehicle adhered to the specifications outlined in SAE J2954 at 3.7 kW (WPT1). Note that the computational results are scalable to other transfer power. Figure 2 shows a detailed schematic of the WPT coils. The transmitting coil was rectangular, with a length of 580 mm and a width of 420 mm following to SAE J2954 [16]. It consisted of 15 turns, with a width of 3 mm. The receiving coil was a 320 mm square. It equipped with 20 turns and had a width of 2 mm. The distance between the top of the transmitting coil and the bottom of the receiving coil was 150 mm, which is in accordance with WPT1. The two coils were assumed to be composed of a perfect conductor for conservative assessment. The thicknesses of shield plate and ferrite core are 2 mm and 3 mm, respectively. The transmitter and receiver current sources \(I_{1}\) and \(I_{2}\), were set to 16 and 17 A, respectively, to achieve a transmitting power of 3.7 kW. The phase difference of the currents between the transmitting and receiving coils was 90\({}^{\circ}\). The frequency of the WPT system was 85 kHz. The following relationship holds for current source \(I_{1}\) and \(I_{2}\)[48].  
\[I_{2}\approx-j\sqrt{\frac{L_{1}}{L_{2}}}I_{1} \tag{1}\]  
where \(L_{1}\) and \(L_{2}\) represent the inductance of the transmitter and receiver coils, respectively. Note that the assumption of coil material as perfect conductor would result in a slightly larger leaked magnetic field of 1% or less, under the condition that the transmitting power is fixed at 3.7 kW [49].  
Figure 1: Japanese adult male model TARO: (**a**) standing and (**b**) sitting postures.  
Figure 3 shows a vehicle model and two realistic exposure scenarios for the assessment. The simplified vehicle's geometry was developed using the Toyota Motor Corporation's Prius model and was positioned in free space. Note that the effect of the ground and surrounding objects marginally influences the magnetic field where the quasi-magnetostatic approximation is valid. The receiving coil was positioned beneath the center of the vehicle body. Misalignment between the receiving and transmitting coils were chosen as 75 mm and 100 mm in the \(x\) and \(y\) directions, respectively, following SAE J2954 [16]. We considered two vehicle body materials, including iron and carbon fiber-reinforced plastic (CFRP). The relative permittivity, permeability, and conductivity values for iron and CFRP were 1, 4000, and 10.3 \(\times\) 10\({}^{6}\) S/m and 1, 1, and 0.25 \(\times\) 10\({}^{6}\) S/m, respectively. The thicknesses of iron and CFRP were 0.5 and 2.0 mm, respectively. In this study, two scenarios discussed in IEC JWG 63184 were considered. In the first scenario, a human body model stands outside the vehicle body where the highest exposure to the magnetic field from the WPT system was computed. Meanwhile, the human body in the second scenario was located in the driver's seat, where the distance from the floor to the driver's buttocks was 200 mm. Note that the position of the human body in the vehicle cabin has been standardized for such purposes [23; 24; 50].  
Figure 2: Schematic of WPT coils (unit: mm): (a) transmitting coils, (b) receiving coils, and (c) positions.