## 1 Introduction  
Carbon fiber-reinforced polymer (CFRP), as a continuously evolving composite material, exhibits numerous advantageous properties, including high specific strength, elevated specific modulus, exceptional fatigue resistance, and remarkable corrosion resistance [1]. It possesses excellent stability and strong acid resistance and is capable of withstanding the corrosion and immersion of concentrated hydrochloric acid and sulfuric acid, among its other merits [2]. The CFRP prepreg is composed of reinforcing fibers and matrix resin and serves as an intermediate product of CFRP articles. Carbon, as the reinforcing agent, exhibits preferable stiffness and tensile properties, undertaking the majority of the load. Epoxy resin, as the matrix, adheres the carbon fibers together through the adhesive effect, thereby facilitating uniform load transfer throughout the entire CFRP. Despite the numerous outstanding characteristics of CFRP, the complexity of its processing technology, production process factors, and external environmental factors may result in the occurrence of defects in CFRP components [3]. Low molecular impurities, solvents, and moisture in the prepreg can easily cause changes in the carbon content and resin content of the CFRP prepreg. Nevertheless, the carbon content and resin content within the CFRP prepreg will exert an influence on various properties of CFRP, resulting in the CFRP failing to reach the prescribed performance standards [4]. In their experiments, [PERSON] et al. discovered that the resistivities in the longitudinal, transverse, and thickness directions of the unidirectional carbon fiber plate would increase significantly with the decrease in the fiber volume fraction. Moreover, the growth rate of the conductivities in the transverse and thickness directions was faster than that in the longitudinal direction [5]. Since the quantity of carbon content can influence the performance of CFRP, carbon content detection is a very crucial link in the production process of prepreg. The performance of the composite material can be enhanced by controlling the quality of the prepreg. The traditional matrix acid etching method is a carbon fiber surface density detection approach based on the chemical differences in components. However, it suffers from drawbacks such as complex processes, high randomness of results, and operational hazards, which are unfavorable for the improvement of the CFRP prepreg production process. Hence, the development of a novel, reliable, simple, and safe carbon fiber surface density detection technology that does not damage raw materials represents an important development direction in the CFRP preparation industry. The development of nondestructive testing technologies for CFRP materials is of significant importance. CFRP prepreg is composed of carbon fibers and a resin matrix, demonstrating multiphase and anisotropic properties. Therefore, it is impossible to infer the rules of the internal eddy current distribution and coil impedance variation based on experience. It is necessary to conduct research through a combination of test analysis and numerical calculation. In recent years, numerous scholars have conducted significant work on electrical property analysis, numerical analysis, and eddy current detection in composite materials. To enhance the sensitivity of the detection coil, various coil structures have been designed for the nondestructive testing of carbon fiber-reinforced composites. [PERSON] et al. employed a testing system featuring differential sensors with two pairs of vertically oriented excitation coils and utilized a central pickup coil for inspecting anisotropic structural materials. To identify a device applicable for detecting hidden defects in such materials, a sample fabricated from quadrupolar woven carbon fiber-reinforced composite material with two artificial defects (the maximum relative depths of the notches were 30% and 70%, respectively, with a thickness of 0.4 mm and a length of 5 mm) was adopted to evaluate this system [6].