The flux through each patch is equal to the normal (perpendicular) component of the field F

n


(

x

)
=
F
(

x

)
cos
⁡
θ


{\displaystyle F_{n}(\mathbf {x} )=F(\mathbf {x} )\cos \theta } at the patch's location x



{\displaystyle \mathbf {x} } multiplied by the area d
S


{\displaystyle dS} . The normal component is equal to the dot product of F

(

x

)


{\displaystyle \mathbf {F} (\mathbf {x} )} with the unit normal vector n

(

x

)


{\displaystyle \mathbf {n} (\mathbf {x} )} (blue arrows)