Question

What is the flux of a vector through a given area in the a vector through field?

Answer 1

Flux (Surface Integrals of Vectors Fields) Suppose the velocity of a fluid in xyz space is described by the vector field F(x,y,z). Let S be a surface in xyz space. The flux across S is the volume of fluid crossing S per unit time

Answer 2

The flux of a vector through a given area in the vector through the field is the volume of the field passing through an area.

• Let A be the area is described by the vector field F(x,y,z). The flux across A is the volume of the field lines crossing the area A per unit time.
• Flux is given by the formula =  $\int\limits_b {(F . n)} \, dA$ , where F is the vector function, n denotes the unit normal vector to the area A.

• The larger the area, the more field lines go through it, the greater the flux.
• Similarly, the stronger the vector field is, the greater the flux.