To understand the definition of electric flux, and how to calculate it. flux is the amount of a vector field that "flows" through a surface. we now discuss the electric flux through a surface (a quantity needed in gauss's law): φe=∫e⃗ ⋅da⃗ , where φe is the flux through a surface with differential area element da⃗ , and e⃗ is the electric field in which the surface lies. there are several important points to consider in this expression: it is an integral over a surface, involving the electric field at the surface. da⃗ is a vector with magnitude equal to the area of an infinitesmal surface element and pointing in a direction normal (and usually outward) to the infinitesmal surface element. the scalar (dot) product e⃗ ⋅da⃗ implies that only the component of e⃗ normal to the surface contributes to the integral. that is, e⃗ ⋅da⃗ =∣∣e⃗ ∣∣∣∣da⃗ ∣∣cos(θ), where θ is the angle between e⃗ and da⃗ .