This interactive demonstration provides an enhanced visualization of flux, moving beyond simple vector projections to a more accurate geometric representation.
- Geometric Flux Representation: The demo creates a transparent, parallelepiped-like shape. This shape represents the volume of substance passing through the surface, directly corresponding to the geometric interpretation of flux.
- Dynamic Volume: As you adjust the velocity vector ($v(x)$) using the sliders, the swept volume dynamically resizes and reorients in real-time. This allows you to directly see how the flux (the volume) changes with the magnitude and direction of the flow.
- Intuitive Relationship to the Dot Product: The height of the 3D volume, measured along the surface normal direction, is directly proportional to the dot product, $v(x) \cdot n$. This visually reinforces the mathematical concept that the flux is determined by the component of the velocity perpendicular to the surface.
- Zero Flux Visualization: When the velocity vector is parallel to the surface, the volume shrinks to zero, providing a clear visual representation of the concept of zero flux.
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Flux as Volume Demonstration