Effect of Magnet Spacing on Magnetic Field Linearity in Selected Commercial Rectangular Magnets

Year 2026, Volume: 30 Issue: 1 , 106 - 113 , 24.04.2026

Samed Gümüş , Yavuz Öztürk

https://doi.org/10.19113/sdufenbed.1789977

https://izlik.org/JA53HC37EX

Abstract

In density measurements using magnetic levitation and in magnetic sensor applications, the linearity of the magnetic field and magnetic force is important for measurement convenience. In line with this purpose, an analysis was conducted on a sample magnet configuration with dimensions of 3×60×10 mm to show influence of magnet spacing on the magnetic field linearity. Additionally, the most commonly used magnet dimensions in industry were selected, and the analyses were repeated for each set individually. For each configuration, the distance between the magnets varied between 1 mm and 10 mm, and for each distance, the magnetic field distribution along the magnetization direction on the central axis of the magnets was calculated and fitted to a linear function. Linearity in these fitting processes was evaluated using the R² and rmse metrics. The highest value of R² = 0.9999 and lowest value of rmse=0.25 mT was obtained for the magnet spacing of 2 mm.

Keywords

Bar Magnet , Magnetic Levitation , Magnetic field linearity

Mıknatıs Aralığının Manyetik Alan Doğrusallığına Etkisinin Ticari Dikdörtgen Mıknatıslarda İncelenmesi

https://izlik.org/JA53HC37EX

Abstract

Manyetik levitasyon kullanılarak yapılan yoğunluk ölçümlerinde ve manyetik sensör uygulamalarında, manyetik alanın ve manyetik kuvvetin doğrusallığı ölçüm kolaylığı açısından önemlidir. Bu amaca uygun olarak, manyetik alan doğrusallığı üzerindeki mıknatıslar arası mesafenin etkisini göstermek için 3×60×10 mm boyutlarında örnek bir mıknatıs konfigürasyonu üzerinde bir analiz yapılmıştır. Ek olarak endüstride sıklıkla kullanılan ticari mıknatıs boyutları seçilerek aynı analizler tekrarlanmıştır. Her bir konfigürasyon için, mıknatıslar arasındaki mesafe 1 mm ile 10 mm arasında değiştirilmiş ve her mesafe için, mıknatısların merkez ekseni boyunca manyetizasyon yönündeki manyetik alan dağılımı hesaplanmış ve doğrusal bir fonksiyona uydurulmuştur. Bu uydurma süreçlerindeki doğrusallık, R² ve rmse metrikleri kullanılarak değerlendirilmiştir. R² = 0.9999 en yüksek değeri ve rmse = 0.25 mT en düşük değeri 2 mm’lik mıknatıs aralığı için elde edilmiştir.

Keywords

Çubuk Mıknatıs , Manyetik Levitasyon , Manyetik alan doğrusallığı

References

• [1] Delikoyun, K., Yaman, S., Yilmaz, E., Sarigil, O., Anil-Inevi, M., Telli, K., et al. 2021. HologLev: A hybrid magnetic levitation platform integrated with lensless holographic microscopy for density-based cell analysis. ACS Sensors, 6(6), 2191–2201.
• [2] Gao, Q.H., Song, P.H., Zou, H.X., Wu, Z.Y., Zhao, L.C., Zhang, W.M. 2025. Three-dimensional manipulation via magnetic levitation. International Journal of Mechanical Sciences, 287, 109949.
• [3] Frenea-Robin, M., Marchalot, J. 2022. Basic principles and recent advances in magnetic cell separation. Magnetochemistry, 8(1), 11.
• [4] Zhang, C., Zhao, P., Wen, W., Xie, J., Xia, N., Fu, J. 2018. Density-based cell analysis using magnetic levitation. Polymer Testing, 70, 520–525.
• [5] Subramaniam, A.B., Yang, D., Yu, H.D., Nemiroski, A., Tricard, S., Ellerbee, A.K., et al. 2014. Noncontact orientation of objects in three-dimensional space using magnetic levitation. Proceedings of the National Academy of Sciences, 111(36), 12980–12985.
• [6] Kartal, R.B., Arslan Yildiz, A. 2024. Exploring neuronal differentiation profiles in SH-SY5Y cells through magnetic levitation analysis. ACS Omega, 9(13), 14955–14962.
• [7] Xie, J., Zhang, C., Gu, F., Wang, Y., Fu, J., Zhao, P. 2019. An accurate and versatile density measurement device: Magnetic levitation. Sensors and Actuators B: Chemical, 295,
• [8] Netzer, Y. 1981. A very linear noncontact displacement measurement with a Hall-element magnetic sensor. Proceedings of the IEEE, 69(4), 491–492.
• [9] Roumenin, C.S., Lozanova, S.V. 2007. Linear displacement sensor using a new CMOS double-Hall device. Sensors and Actuators A: Physical, 138(1), 37–43.
• [10] He, Q., Fan, S., Chen, N., Tan, R., Chen, F., Fan, D. 2021. Analysis of inductive displacement sensors with large range and nanoscale resolution. Applied Sciences, 11(21), 10134.
• [11] Hancox, C.I., Doret, S.C., Hummon, M.T., Luo, L., Doyle, J.M. 2004. Magnetic trapping of rare-earth atoms at millikelvin temperatures. Nature, 431(7006), 281–284.
• [12] Anil-Inevi, M., Yaman, S., Yildiz, A.A., Mese, G., Yalcin-Ozuysal, O., Tekin, H.C., Ozcivici, E. 2018. Biofabrication of in situ self-assembled 3D cell cultures in a weightlessness environment generated using magnetic levitation. Scientific Reports, 8(1), 7239.
• [13] Camacho, J.M., Sosa, V. 2013. Alternative method to calculate the magnetic field of permanent magnets with azimuthal symmetry. Revista Mexicana de Física E, 59(1), 8–17.
• [14] Edwards, C., Palmer, S.B. 1986. The magnetic leakage field of surface-breaking cracks. Journal of Physics D: Applied Physics, 19(4), 657.
• [15] Anil-Inevi, M., Sarigil, O., Unal, Y.C., Tekin, H.C., Mese, G., Ozcivici, E. 2025. Magnetic levitation-based determination of single-nuclei density. Biomaterials Advances, 214581.
• [16] Shah, A.S., Karabulut, M.A. 2022. Reliability estimation for drone communications by using an MLP-based model. International Advanced Researches and Engineering Journal, 6(3), 204–210.
• [17] Ergül, B., Yıldız, Z. 2023. Comparison of classical and robust factor analyses methods. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 27(3), 401–410.
• [18] Durmus, N.G., Tekin, H.C., Guven, S., Sridhar, K., Arslan Yildiz, A., Calibasi, G., et al. 2015. Magnetic levitation of single cells. Proceedings of the National Academy of Sciences, 112(28), E3661–E3668.
• [19] Yu, J., Li, D., Zhu, C., Ouyang, Q., Miao, C., Yu, H. 2023. A magnetic levitation system for range/sensitivity-tunable measurement of density. Sensors, 23(8), 3955.
• [20] Zhang, C., Zhao, P., Wen, W., Xie, J., Xia, N., Fu, J. 2018. Density measurement via magnetic levitation: linear relationship investigation. Polymer Testing, 70, 520–525.
• [21] Xie, J., Zhang, C., Gu, F., Wang, Y., Fu, J., Zhao, P. 2019. An accurate and versatile density measurement device: Magnetic levitation. Sensors and Actuators B: Chemical, 295, 204–214.
• [22] Rabie, M., Ibrahim, S.S., Eltawil, A.A., Sayed, B.M. 2025. Investigation of the accurate hybrid automatic magnetic levitation system for measuring the high density of material. Measurement, 118866.
• [23] Anil-Inevi, M., Sarigil, O., Unal, Y.C., Tekin, H.C., Mese, G., Ozcivici, E. 2025. Magnetic levitation-based determination of single-nuclei density. Biomaterials Advances, 214581.