🧄Analyze Flux and Laplacian of The Yukawa Potential

The divergence theorem must be carefully adapted to handle singularities within a volume. While a direct surface integral readily provides the correct physical flux, the divergence theorem's volume integral needs to account for the singularity (like a point charge at the origin) using a delta function to yield a consistent result. This highlights that the Laplacian of a potential is directly linked to the charge density, with the delta function representing a point charge.

🎬how different parameters affect Yukawa Potential and its Vector Field

The visualization illustrates how it visually demonstrates the concept of a screened force. Unlike a long-range force, like electromagnetism, a screened force has a finite range and its influence diminishes rapidly with distance.

🖊️Mathematical Proof

The Yukawa Potential: Analysis of Flux and Laplacian | Proof and Derivationviadean on Notion