## 2 Magnetometer Design
The sensors are powered by a source of DC current, and the reading of the output voltage is taken by a multimeter. (1) We used an acrylic plate of 65 \(\times\) 55 mm with 10.5 mm of thickness, (2) two neodymium magnets of the same configuration containing 12.78 mm thick and 19 mm in diameter, (3) all these are on an iron base containing two screws of the same configuration, (4) a printed circuit board used to operate the sensors plate, (5) an alignment system consisting of a screw and a spring system, (6) an aluminum base, (7) a battery set or a power supply system that can supply the sensors with 5 V DC. (**b**) Circuit board used to use the Hall sensor. 90215 Hall effect sensor (Melexis Inc.), calibrated with a fixed sensitivity of 2.8 mV/mT and an offset of 0.4 V. This sensor is responsible for detecting the magnetic field of magnets in the \(z\)-axis. In this assembly, we used two bench multimeters to detect the two sensors: HP 34401A and Iminipa ET-2042D. To power the Hall effect sensors with 5 V, we can use a battery or a power system connected to the mains. The developed magnetometer can be seen in Figure 3a and all components used can be seen in Figure 3b, as follow: (1) Magnet support base (cylindrical shape) of 30 mm diameter and approximately 109 mm long, (2) aluminum base of 45 \(\times\) 45 mm and 22 cm length, used as a linear rail, (3) two iron threaded nuts to keep the magnets fixed, bring them closer or move them away from the sample, varying thus the applied magnetic field, (4) fixed iron structure to fix the probe Hall, nuts and alignment screw, (5) device built to activate sensors S1 and S2, this device was connected to a multimeter, (6) probe Hall, (7) cylindrical neodymium magnet of 19 mm diameter and 12.9 mm length, (8) and (9) sample holder, acrylic plates of 5.2 \(\times\) 3.1 \(\times\) 32 mm, which is a sample holder that can analyze samples within a cylindrical cavity of 3.0 mm diameter and 3.0 mm length, (10) screw used to align the probe Hall with the magnetic field that can be applied by the magnets, (11) multimeter used for reading Hall sensors. The AD-AD22151 Hall effect sensor was calibrated to maximum sensitivity (110 mV/mT) Figure 3a. The calibration curve is shown in Figure 4a. In this curve, we can observe that the Hall sensor has a linear relationship with the induced field voltage and the applied magnetic field. We can also observe that there was no hysteresis in the sensor, which is a result typical of the Hall effect sensor. In addition, we analyzed the signal/noise ratio of the AD22151 sensor at the minimum and maximum sensitivities. The curves are shown in Figure 4b. In this figure, we can see that when AD22151 has a noise of approximately 40 \(\mu\)V. These results identify the noise of the magnetometer reading system, the peak of the graph is related to an AC magnetic field applied at 4.0 Hz. Figure 4c represents a theoretical and experimental graph of the behavior of the magnetic field of the magnet in relation to spatial distance in the \(z\) axis starting from the center of one of the magnet's surfaces, the theoretical curve was obtained using the cylindrical model used by [PERSON] and [PERSON] [14]. In Figure 4c, we can verify that the experimental results are in agreement with the theoretical curve based on Equation (1) taken from the paper published by [PERSON]  
Figure 2: Acrylic plate (probe Hall) in the center with two Hall effect sensors, which have a maximum sensitivity of 110 mV/mT, due to the AD-AD22151 Hall effect sensor. and [PERSON] [14]. Already in Table 1, we can verify the relationship between the magnetic field applied by the magnet and the distance in the \(z\) axis in mm. \[\text{B}(z)=\frac{\mu_{0}m_{z}}{2}\left[\frac{z}{\sqrt{2^{2}+R^{2}}}-\frac{z-L}{ \sqrt{\left(z-L\right)^{2}+R^{2}}}\right] \tag{1}\]  
Figure 3: (**a**) The developed magnetometer.