- #1
ookt2c
- 16
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Homework Statement
Evaluate the flux of F(x,y,z)=xi + yj + zk across the surface q:x^2+y^2+z^2=16, oriented by unit normals.
Flux is a measure of the flow of a quantity through a surface. In mathematical terms, it is the integral of a vector field over a surface.
The flux of a vector field can be calculated by taking the dot product of the vector field and the unit normal vector to the surface, and then integrating this dot product over the surface.
The unit normal vector to a surface is a vector that is perpendicular to the surface at a given point, and has a length of 1.
Positive flux indicates that the vector field is flowing outward through the surface, while negative flux indicates that the vector field is flowing inward through the surface.
Flux is related to divergence through the Divergence Theorem, which states that the flux of a vector field through a closed surface is equal to the volume integral of the divergence of that vector field over the enclosed volume.