Electric flux is the measure of the flow of the electric field through a given area. It is defined as the number of electric field lines passing through a surface. The electric flux is proportional to the electric field strength, the area of the surface, and the cosine of the angle between the electric field and the normal to the surface.

The mathematical expression for electric flux is:

ΦE = E ⋅ A

where:

* ΦE is the electric flux (in units of volt-meters squared per coulomb)
* E is the electric field (in units of volts per meter)
* A is the area of the surface (in units of meters squared)
* ⋅ is the dot product, which represents the product of two vectors
* θ is the angle between the electric field and the normal to the surface

The electric flux is maximum when the electric field is perpendicular to the surface and minimum when the electric field is parallel to the surface.

For example, consider a plane surface placed in a uniform electric field. If the plane is perpendicular to the electric field, then the electric flux through the plane is maximum. If the plane is parallel to the electric field, then the electric flux through the plane is zero.

The electric flux can also be used to calculate the total charge enclosed by a closed surface. The Gauss's law states that the total electric flux through a closed surface is equal to the net charge enclosed by the surface divided by the permittivity of free space.

∮ E ⋅ dA = q/ε0

where:

* ∮ means "the integral over"
* dA is a small area element on the closed surface
* q is the total charge enclosed by the surface
* ε0 is the permittivity of free space (8.854 × 10^−12 F/m)