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

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

{% embed url="<https://youtu.be/_-ApCjUv1mM>" %}

#### Condensed Notes

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