Flux à travers une surface

Let's now consider the concept of the flux of a vector field on a surface.

The flux, denoted by the subsymbol , is an integral over a surface of the scalar product `ads`, that is, the scalar product between the vector field and an element of an elementary surface. We distinguish two types of surfaces: open surfaces and closed surfaces. We will first address the concept of a closed surface. Imagine a volume `v` closed by a

surface, a ball for example. At any point on a closed surface, I can define an elementary surface vector, which I call `ds`. The property of this elementary surface vector is that it is always orthogonal to the surface surrounding the volume, and also that it is always directed outwards.

The flux of a vector field through a closed surface is denoted by the double integral crossed by a circle, which indicates that the surface is closed on itself. This means that it surrounds a volume that extends from `ds` to scalar `ds`. Now, there is a second type of surface: the concept of open surfaces, which is based on a boundary.

Let's imagine a contour. Close it. I've drawn a circular contour with a solid line representing the part coming towards you and a dotted line representing the part behind the screen. You can actually press on an infinite number of surfaces on this contour. The simplest surface you can press on is the disk, whose border is the contour. You

can also press on this contour. Close an open surface. Imagine a beanie or a hat. The surface of the beanie or the surface of the hat constitutes an open surface, and this surface will rest on a closed tachometer, which is the contour that will actually go around your head. In this case [Music] How are we going