🎬Only the component of the current density vector that is exactly perpendicular to the surface contri

Only the component of the current density vector that is exactly perpendicular to the surface contributes to the flux

The demo visually illustrates the concept of vector flux, showing that the flow crossing a surface is determined exclusively by the component of the current density vector ( $J$ ) that is perpendicular to the surface ( $J_{\perp}$ ), which is mathematically captured by the scalar product $J$ . $n$. As the $J$ vector rotates $360^{\circ}$ around the origin, the animation dynamically updates its decomposition, making it clear that when $J$ points predominantly outward (acute angle with the normal $n$ ), the flux is positive (outflux), and when $J$ points inward (obtuse angle with $n$ ), the flux is negative (influx). The flux drops to zero precisely when $J$ is tangential to the surface, as the perpendicular component $J_{\perp}$ vanishes entirely at that orientation.

Narrated Video

Condensed Notes

Only the component of the current density vector that is exactly perpendicular to the surface contributes to the flux | Animated Resultsviadean on Notion