Скачать или смотреть Analysis of Dipole Field Dynamics From Potentials to Particle Trajectories

Proof and Derivation: https://viadean.notion.site/Analysis-...

Summary: This study integrates mathematical theory with computational dynamics by analyzing the dipole field through four interconnected lenses. It begins by mapping the scalar potential $\Phi$ to establish an energy topography that dictates electrostatic interactions and follows with a visualization of the vector potential $\vec{A}$ to confirm the field's solenoidal nature. The investigation then transition to a numerical verification of energy conservation ($E = K + \Phi$), providing empirical proof of the field's conservative properties via Helmholtz decomposition. Finally, the project culminates in a dynamical simulation of particle trajectories, demonstrating how the unique $1/r^3$ force and its angular dependence create complex, non-central orbital paths that distinguish dipole interactions from simpler central-force laws.