## 3 Finite Element Simulation Analysis of Electromagnetic Field
### Research on Geometric Parameters of the Probe  
The structure and parameter design of eddy current detection sensors is of paramount importance for ensuring efficient and accurate nondestructive testing. As the design of the sensor directly determines its capacity for detecting material defects, its sensitivity, and its penetration depth. In the detection of CFRP prepregs in this paper, considering the properties of CFRP, the expected detection accuracy, and the convenience of practical operation, parameters such as the geometric parameters of the coil and the lift-off height between the probe and the tested material are optimized. Based on this model, the relationship between the coil impedance and the working frequency, number of turns, diameter, inner diameter, height of the excitation coil, and the lift-off height between the probe and the tested material is studied. Hereby, the influence of the coil's geometric parameters on the sensor's sensitivity and linear range is investigated. Separate simulation experiments were conducted by varying the number of coil turns (from 20 to 100 with a step of 10) at excitation frequencies ranging from 1 to 10 MHz (with a step of 1 MHz). The experimental results are depicted in Figure 5. When the excitation frequency is 1 MHz, the impedance difference between a 20-turn coil and a 50-turn coil is 0.53 \(\Omega\), and the impedance difference between a 20-turn coil and a 100-turn coil is 2.38 \(\Omega\). When the excitation frequency is 10 MHz, the impedance difference between a 20-turn coil and a 50-turn coil is 48.93 \(\Omega\), and the impedance difference between a 20-turn coil and a 100-turn coil is 223.61 \(\Omega\). Apparently, with the increase in the excitation frequency and the number of coil turns, the gradient of the coil impedance change gradually increases. In particular, when the number of coil turns exceeds 50, the coil impedance change becomes more significant. The coil inductance Equation (13) helps to improve our understanding of the conclusions related to coil design. However, an increase in the number of coil turns will enhance the magnetic field strength, and excessive turns may lead to signal attenuation. \[L=\frac{\mu\cdot N^{2}\cdot\text{Area}}{\text{length}} \tag{13}\]  
Figure 5: The relationship between the excitation frequency, the number of coil turns, and the coil impedance. In Equation (13), \(L\) is the inductance of the coil, \(\mu\) is the magnetic permeability, \(N\) is the number of turns in the coil, area is the cross-sectional area of the coil, and length is the length of the coil. Figure 6 presents the distribution diagrams of the magnetic flux density modulus at excitation frequencies of 1 MHz and 10 MHz, respectively. By comparing the two diagrams, we can see that low-frequency signals penetrate the inspected material more deeply, making them suitable for detecting deep defects. In contrast, high-frequency signals are better for detecting surface or small defects. By Equation (14), we can better understand that as frequency increases, the standard penetration depth decreases. This relationship highlights how higher frequencies cause the current to concentrate near the surface of the material, a phenomenon known as the skin effect. The skin depth \(\delta\) is inversely proportional to the square root of the frequency, meaning that as frequency \(f\) increases, \(\delta\) becomes smaller. This effect is crucial in applications such as nondestructive testing, where changes in penetration depth impact the accuracy of subsurface evaluations. Our method of detecting carbon fiber prepregs can only achieve depths of 1-2 mm, which is considered surface detection. Therefore, the simulation experiments in the following text use an excitation frequency of 10 MHz. \[\delta=\frac{1}{\sqrt{\pi\cdot\mu\cdot\sigma\cdot f}} \tag{14}\]  
\(\delta\) is the skin depth, \(\mu\) is the magnetic permeability of the material, \(\sigma\) is the electrical conductivity, and \(f\) is the frequency of the alternating current.