A Simple Numerical Model for Exploring Electrostatic Principles: A Multipole Simulation

Yıl 2025, Cilt: 3 Sayı: 2, 100 - 107, 31.12.2025

Nayan Bhandari Aratrika Mal

https://doi.org/10.26650/PAR.2025.00011

https://izlik.org/JA72SN33KP

Öz

The multipole expansion is a foundational yet conceptually challenging topic in electrostatics. To bridge this pedagogical gap, we present a computational model designed to visualize the fundamental behavior of electric fields originating from various multipole configurations. Based on the superposition principle for discrete charges, the model simulates dipoles, tripoles, quadrupoles, and pentapoles, and calculates the resulting electric field magnitude as a function of distance (𝑟). The results confirm the core theoretical prediction: the power-law decay of the field, given by 𝐸 ∝ 1/𝑟𝑛+2, becomes progressively steeper for higher-order multipoles. This work serves as an effective pedagogical tool, demonstrating how computational physics can render abstract theories tangible and thereby enhance the intuitive understanding of fundamental physical principles. Besides this also provides a platform for further exploration, enabling users to extend the model to more complex configurations and compare computational results with analytical predictions in a systematic manner.

Anahtar Kelimeler

Physics education , computational physics , electrostatics , electric multipoles , numerical simulation , visualisation

Kaynakça

• Atkins P., de Paula J., Keeler J., 2018, Atkins’ Physical Chemistry, 11th edn. Oxford University Press google scholar
• Byczuk K., Jakubczyk P., 2023, American Journal of Physics, 91, 840 google scholar
• Chabay R. W., Sherwood B. A., 2008, American Journal of Physics, 76, 327 google scholar
• Chen P., Yang Z. Q., Shi Z. Z., Hou Q. Y., Jin G. R., 2024, American Journal of Physics, 92, 78 google scholar
• Cross R., 2025, European Journal of Physics google scholar
• Griffiths D. J., 2017, Introduction to Electrodynamics, 4th edn. Cambridge University Press google scholar
• Harris C. R., et al., 2020, Nature, 585, 357 google scholar
• Hunter J. D., 2007, Computing in Science & Engineering, 9, 90 google scholar
• Jackson J. D., 1999, Classical Electrodynamics, 3rd edn. Wiley google scholar
• Jacobs R., Morgan D., et al., 2025, Current Opinion in Solid State and Materials Science google scholar
• Jones M. R., 2001, Idealization in Contemporary Physics, 63, 173 google scholar
• Koulouridis S., 2025, Materials, 18, 2344 google scholar
• Krasnova L., et al., 2025, ResearchGate Preprint google scholar
• Lineweaver C. H., Patel V. M., 2024, American Journal of Physics, 92 google scholar
• Mazibe E. N., Gaigher E., Coetzee C., 2023, Eurasia Journal of Mathematics, Science and Technology Education, 19, em2241 google scholar
• Moreira V. C., Gavião W. D., 2020, Revista Brasileira de Ensino de Física, 42, e20190306 google scholar
• Murray A. J., Hickman C., 2023, American Journal of Physics, 91, 847 google scholar
• Odden T. O. B., et al., 2025, in 2025 Physics Education Research Conference Proceedings. AAPT google scholar
• Puntel M., Gonçalves G. S., Kern D. P., 2021, Revista Brasileira de Ensino de Física, 43, e20200424 google scholar
• Reed B. C., 2024, American Journal of Physics, 92 google scholar
• Sullivan K. D., Sen A., Sullivan M. C., 2023, American Journal of Physics, 91 google scholar
• Tartero G., Krauth W., 2024, American Journal of Physics, 92, 65 google scholar
• Taylor J. R., 1997, An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, 2nd edn. University Science Books google scholar
• Thorne K. S., 1980, Reviews of Modern Physics, 52, 299 google scholar
• Umrigar C. J., Anderson T. A., 2024, American Journal of Physics, 92 google scholar
• Van Rossum G., Drake Jr. F. L., 2009, Python 3 Reference Manual. CreateSpace, Scotts Valley, CA google scholar
• Wieman C. E., Adams W. K., Perkins K. K., 2008, Science, 322, 682 google scholar
• Zhuang Y., et al., 2025, AIAA Journal google scholar
• van Dijk W., 2023, American Journal of Physics, 91, 826 google scholar