## 4 Verification Experiment  
To verify the correctness of the theoretical simulation, the rectangular magnetic dipole used in the simulation was used in an experiment to maintain the magnetic moment parameters unchanged. The three components of its magnetic moment were 0.51 A\(\cdot\)m\({}^{2}\), 6.70 A\(\cdot\)m\({}^{2}\), and 0.66 A\(\cdot\)m\({}^{2}\). It was attached to a copper rod in the direction of the magnetic moment 0.66 A\(\cdot\)m\({}^{2}\) component and placed in a seawater pool. With the copper rod as an axis, it was manually rotated on the seawater surface (no difference from underwater rotation because of the consistent magnetic conductivity between seawater and air). An electric field measurement system was fixed underwater. The seawater in the pool was prepared with sea salt to achieve a conductivity of approximately 2.8 S/m. In the electric field detection system, considering the actual engineering application background, the sensor uses six Ag/AgCl electrodes (Ag/AgCl electrodes have the advantages of better stability, lower sub-noise, etc., as a reference electrode is widely used in the ship's anti-corrosion system, and can be underwater for more than ten years of continuous work), constructing a three-component electric field measurement system. Here, two electrodes are in the same direction as a group of electrode pairs and each pair is perpendicular to each other. The distance between the measuring electrodes and the reference electrode in the x, y, and z directions in the measurement system is 10 cm, the water depth of the experimental pool is 85 cm, the reference electrode is 30 cm from the water surface, and  
Figure 5: Electric field induced by a sloshing magnetic dipole at \(\pi/3\) for (**a**) \(E_{x}\), (**b**) \(E_{y}\), and (**c**) \(E_{z}\). (**a**) \(E_{x}\) component of an induced electric field, (**b**) \(E_{y}\) component of an induced electric field, and (**c**) \(E_{z}\) component of an induced electric field. the horizontal distance between the magnet and the reference electrode is 5 cm (the sensor needs to be immersed in salt water before the experiment to stabilize the polar deviation). The signals measured by the electric field acquisition system were amplified, filtered, and conditioned, and then collected and stored by the data acquisition card, with a sampling frequency of 20 Hz. It was measured that the rotational velocity was approximately \(\omega\approx 5\pi\) rad/s since the magnetic dipole was manually rotated. The schematic diagram of the experiment is shown in Figure 6. The theoretical and measured values were compared, as shown in Figure 7.  
Based on the analysis of experimental results in Figure 7, it was concluded that:  
1. The measured and theoretical values of the electric field induced by a rotating magnetic dipole were basically equal in terms of scale and phase characteristics. The difference between them must be mainly attributed to the manual rotation in the experiment, causing the fluctuation of rotational velocity. 2. Based on the measured results, the phase difference between \(\mathbf{E}_{y}\) and \(\mathbf{E}_{x}\) was \(\pi/2\), and the phase difference between \(\mathbf{E}_{z}\) and \(\mathbf{E}_{y}\) was \(\pi\). These values are consistent with the theoretical analysis. The above experimental results demonstrate the correctness of the mathematical models and theoretical analysis. Due to the limitations of experimental conditions, the experiment on the induced electric field generated by magnet oscillation in Section 2.2 was limited. Due to the difficulty in maintaining and controlling the oscillation angles \(\pi/6\) and \(\pi/3\) during manual oscillation, mechanical oscillation equipment can generate significant mechanical noise and irremovable electromagnetic interference during the oscillation process.