Читать книгу Stigmatic Optics - Rafael G González-Acuña - Страница 14

An initial concept needed to enter Maxwell’s equations entirely is electric flux. The electric flux, or electrostatic flux, is a scalar quantity that expresses a measure of the electric field that passes through a defined surface, or expressed in another way, is the measure of the number of electric field lines that penetrate a surface.

The portion of electric flux dΦE⃗ through an infinitesimal area da is given by,

dΦE⃗=E⃗·n⃗da.(1.4)

The electric field E⃗ is multiplied by the component of the area perpendicular to the field. n⃗ is the normal unit vector of the infinitesimal area da.

The electric flux through a surface S is therefore expressed by the surface integral,

ΦE⃗=∫SE⃗·n⃗da,(1.5)

where E⃗ is the electric field and n⃗da is the differential surface vector that corresponds to each infinitesimal element of the entire surface S. Please see figure 1.4.

Figure 1.4. Flux of an electric field through a surface. On the right the normal vector n⃗ of the surface is parallel to the electric field E⃗. On the left there is inclination on the surface. Thus, there is an angle between n⃗ and E⃗.