Question

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

Answer 1

The flux of a vector field \[[\vec{F}]\] through a surface [S] is the surface integral \[[\Phi=\int_{S}\vec{F}\cdot d\vec{A}]\], where \[[d\vec{A}]\] is the directed area element. For a uniform field through a flat area, \[[\Phi=FA\cos\theta]\], with \[[\theta]\] the angle between the field and the area normal.