Conical flux by closing with a cap (source code)

= Conical flux by closing with a cap

To evaluate outward <flux> through the lateral surface of a finite <right circular cone>, add its planar cap and apply the <divergence theorem> to the enclosed solid. Subtract the cap flux, whose outward normal points away from the solid. For a cone $r=az$ with $0\leq z\leq h$, the volume element is $r\,dr\,d\varphi\,dz$ and the cap has radius $ah$. The cone's vertex has no unique normal, but is a set of area zero; one can remove a small tip and take a limit when the field is regular there.