Читать книгу Stigmatic Optics - Rafael G González-Acuña - Страница 16

Gauss’s law for magnetism has the same structure as the Gauss law of the previous section with the condition that there are no magnetic charges.

So, we start with the definition of magnetic flux through a surface S,

ΦB⃗=∫SB⃗·n⃗da,(1.10)

the magnetic field, B⃗, multiplied by the component of the area perpendicular to the field, where n⃗ is the unit normal vector of infinitesimal area da.

Therefore, over a closed surface S, Gauss’s law of magnetism is given by

∮SB⃗·n⃗da=0,(1.11)

As we mentioned in the introduction, there are no magnetic charges. What Gauss’s law of magnetism tells us is that the total magnetic flux passing through any closed surface is zero.

Tacking the knowledge acquired in the last section, we can get the vector form of Gauss’s law of magnetism, hence,

∇·B⃗=0.(1.12)

This happens, as expected because there are no magnetic charges. Therefore, the density of magnetic charge is zero.