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

Year 2025, Volume: 3 Issue: 2, 100 - 107, 31.12.2025

Nayan Bhandari Aratrika Mal

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

https://izlik.org/JA72SN33KP

Abstract

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.

Keywords

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

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