🧄The Uniqueness Theorem for Vector Fields

The Uniqueness Theorem for Vector Fields is a cornerstone of physics and engineering, proving that a vector field is uniquely defined by its "fingerprint"—a combination of its divergence (sources), curl (circulations), and normal component on the boundary. This is intuitively demonstrated by showing that any two fields with matching fingerprints must be identical, as an animation can smoothly transform one into the other, visually confirming the theorem's validity.

🎬two vector fields are initially different but share the same divergence curl boundary conditions

The interactive demo visually illustrates the core principle of the Uniqueness Theorem for vector fields. While a mathematical proof can be abstract, the animation provides an intuitive understanding that a vector field is uniquely defined by its divergence, curl, and its normal component on the boundary. The ability to smoothly transform a second, different-looking field into the first one by matching these properties serves as a powerful visual confirmation of the theorem's validity.

🖊️Mathematical Proof

The Uniqueness Theorem for Vector Fields | Proof and Derivationviadean on Notion