Gauss theorem in the presence of dielectric is an important basic principle in electricity. When there is a dielectric near the charged body, the dielectric molecules are polarized and act on the electric field. According to Gauss theorem, the ratio of electric flux density to space charge density is always equal to the integral of the normal component of the electric field closed surface in this area in space. It is expressed as: ∮ s d dS = q, where d is the electric displacement vector, the symbol d is the point multiplication, dS is the area of the infinitesimal element at any point on the closed surface S, and q is the total charge in the closed surface S. ..

When there is a dielectric, the amount of charge will not change, but the electric field intensity will change due to the polarization of the dielectric, so the distribution of electric field intensity under the influence of the dielectric should be considered when calculating the potential. Due to the polarization effect of dielectric, free charges will appear on the surface of conductor to produce polarized charges, thus changing the charge density. In fact, in some cases, we can assume that there is no free charge density εfree in the dielectric. Then, Gauss theorem can be simplified as follows: ∮ s ε e ds = q, where ε is dielectric constant, e is electric field strength, q is total charge in closed surface S, and S is closed surface. Gauss theorem provides a method to calculate the electric field intensity around charged bodies. The electric field intensity can be expressed as such a mathematical expression by Gaussian area method, which enables us to solve the electric field intensity under some simple geometric figures. Combining with specific problems, choosing appropriate calculation methods can greatly simplify the process of solving problems.

In a word, Gauss theorem in the presence of dielectric is an indispensable tool in electricity, which plays an important role in studying the distribution of electrostatic field and its related problems, such as capacitance and field energy. In practical engineering, it is widely used in high voltage insulation technology, electronic technology, power system and radar technology.