23.1: Electric Flux
The concept of flux describes how much of something goes through a given area. More formally, it is the dot product of a vector field within an area. For a better understanding, consider an open rectangular surface with a small area that is placed in a uniform electric field. The larger the area, the more field lines go through it and, hence, the greater the flux; similarly, the stronger the electric field (represented by a greater density of lines), the greater the flux. On the other hand, if the area is rotated so that the plane is aligned with the field lines, none will pass through, and there will be no flux. If the area is perpendicular to the electric field then the angle between their vectors becomes zero, resulting in maximum flux. Suppose the surface is rotated in such a way that it forms a 60° angle with the electric field; in this case, the electric flux results in half of the product of the electric field multiplied by the area.
For discussing the flux of a vector field, it is helpful to introduce an area vector. This vector has the same magnitude as the area and is directed normal to that surface. Since the normal to a flat surface can point in either direction from the surface, the direction of the area vector of an open surface needs to be chosen. However, if a surface is closed, then the surface encloses a volume. In that case, the direction of the normal vector at any point on the surface is from the inside to the outside.
The electric flux through an surface is then defined as the surface integral of the scalar product of the electric field, and the area vector and is represented by the symbol Φ. It is a scalar quantity and has an SI unit of newton-meters squared per coulomb (N·m2/C). In general, a rectangular surface is considered an open surface as it does not contain a volume, and a closed surface can be a sphere as it contains a volume.
