🎬Visualizing the Dipole-Field Line Geometry and Singular Flow Dynamics

The two demonstrations illustrate the transition from a theoretical point-dipole to a physically consistent model by contrasting the exterior "butterfly" geometry with the necessary internal continuity. While the first demo establishes that the far-field drops off as $1 / r^3$ and points downward along the z-axis, the second animation reveals that these field lines must "snap" upward through the source to form closed loops. This distinction proves that the magnetic field is truly solenoidal ( $\nabla \cdot B=0$ ), where the singular "upward" flow at the core perfectly balances the external return flow, visually resolving the mathematical singularity through the lens of a finite, physical current loop.

🎬Narrated Video

🧵Related Derivation

🧄Computing the Magnetic Field and its Curl from a Dipole Vector Potential (MFC-DVP)

⚒️Compound Page

Visualizing the Dipole-Field Line Geometry and Singular Flow Dynamics | Resulmationviadean on Notion