## 4 Results and Discussion
### Force Acting on the PM  
In our experiment, we measured two components of the force acting on the PM. One is perpendicular to the sample surface (z), and the other is parallel to it and the same as the direction that  
Figure 4: Original measured signal shown on the oscilloscope and its amplitude (inset). (**a**) The stable amplitude indicates stable amplitude of the force acting on the PM; (**b**) The amplitude is increasing, indicating the amplitude of the force is disturbed. the defect moves along (x). The y-component is not measured because the defect is always located along the \(x\)-axis in our measurement, thus significant change is not observed in the y-component of the force due to symmetry. Figure 5 shows the measured force as the defect is at different positions and in Figure 6 the distribution of the Lorentz force density in the \(z\)-direction is shown and the arrows represent the direction of the Lorentz force density in \(x\)-\(y\) plane. In both Figures 5 and 6, x = 0 refers to the position where the defect aligned with the PM. Figure 5a shows the z-component of the force acting on the PM. The z-component is the perpendicular component of the Lorentz force and yields the most signific  
Figure 5: Experimental and numerical simulation results show that the detection quantities of the z-component and the x-component, the defect is a circular through hole with a diameter of 1 mm. (**a**) z-component and (**b**) x-component. Figure 6: Lorentz force density distribution with the defect present at different positions (**a**) No defect; (**b**) x = -4 mm; (**c**) x = -2 mm; and (**d**) x = 0 mm. The color presents the z-component intensity where the arrow presents the direction and intensity in \(x\)-\(y\) plane. can be observed although only one defect is present. The reason for the two peaks is illustrated in Figure 6. Because of the geometry of the exciting coil, when no defect is present, the Lorentz force density distribution inside the sample yields the shape of a \"ring\" and a locally minimal value appears at the center of the \"ring\" (Figure 6a). When the defect is present, the signal will increase as the defect moves close to this \"ring\", the signal reaches the maximal value as the defect is on top of this \"ring\" (Figure 6b,c). The signal then decreases as the defect moves to the local minimal value (Figure 6d). The leaving process of the defect is completely symmetrical with the change of the \(z\)-direction Lorentz force density during the process of entering, leading to a second peak. The experimental and numerical results are consistent with each other as shown in Figure 5a, and the positions of two peaks are nearly identical with a slight difference caused by experimental error. The reason for the asymmetric experimental result is that the lift-off distance is changed caused by the uneven surface of the testing copper plate. Thus, because of the changed lift-off distance the eddy current is not symmetric in the measurement process, and the force acting on the PM is different at the positions of the two peaks. Compared with the perpendicular direction (\(z\)), force measured in the horizontal direction has not been fully studied. Figure 5b shows the x-component of the force acting on the PM. The measured force is 0 at x = 0 and has two opposite peaks around it. The direction of this x-component Lorentz force density can be either positive or negative as the arrows indicate in Figure 6a, therefore, the defect could cause the net x-component of the Lorentz force density to be either positive or negative (Figure 6b,c). Note that when there is no defect or the defect is located at x = 0, the Lorentz force density in the x-component has a symmetric feature and thus the net force is zero (Figure 6a,d). The experimental results agree with the simulation results as shown in Figure 5b. By measuring the reaction of the Lorentz force, the size of the defects can also be quantitatively evaluated. Figure 7 shows the measured force acting on the PM for defects of various sizes.