What exactly is Gauss s theorem and what is Gauss s theorem?

Gauss's theorem is an aspect of a mathematical theorem, this mathematical theorem is called Gauss's theorem, and this mathematical integral equation is called XX Gauss's theorem in different applications.

The internal electric field strength of the infinitely long uniformly charged cylindrical surface is zero, and the external electric field strength strength is calculated as shown in the figure below.

<> Gauss's theorem, one of the fundamental equations for electrostatic fields, which gives the relationship between the area component of the electric field strength on an arbitrary closed surface and the total electric charge enclosed within the closed surface.

One of the important theorems of vector analysis. The flux through a closed surface is proportional to the amount of charge enclosed by the closed surface. In other words:

The area of the electric field strength on a closed surface is proportional to the amount of charge enclosed by the closed surface, since the magnetic field lines always close the curve, so any magnetic field line entering a closed surface must come out of the surface, otherwise the magnetic field line will not be closed.

If, for a closed surface, the outward direction is defined as a positive normal, then the magnetic flux entering the surface is negative and the magnetic flux coming out is positive, then the total magnetic flux through a closed surface is 0. This law is similar to Gauss's theorem in the electric field, hence it is also known as Gauss's theorem.

It shows that the flux of the electric field strength to any closed surface depends only on the algebraic sum of the charges in the closed surface, and is independent of the distribution of charges in the surface, nor of the charges outside the closed surface. In the case of a vacuum, q is the algebraic sum of the free charges enclosed within the closed surface. When a medium is present, q should be understood as the sum of the free and polarized charges enclosed within the closed surface.

Gauss's theorem reflects the fact that the electrostatic field is an active field. Wherever there is a positive charge, there must be a power line that emits it; Wherever there is a negative charge, there must be a convergence of power lines. The positive charge is the source of the power line, and the negative charge is the tail of the power line.

Gauss's theorem is derived directly from Coulomb's law, which is entirely dependent on the inverse quadratic law of the forces acting between charges. Applying Gauss's theorem to a metal conductor under electrostatic equilibrium conditions, it is concluded that there is no net charge inside the conductor, so determining whether there is a net charge inside the conductor is an important method to test Coulomb's law.

For some symmetrically distributed electric fields, such as the electric field of a uniformly charged ball, the electric field of an infinitely large uniform charged surface, and the electric field of an infinitely long uniformly charged cylinder, the electric field strength of Gauss's theorem can be directly calculated.

Gauss's theorem: make a cylindrical surface with a radius of r and a height of h, the axis of the cylinder coincides with the charged straight line, and the field strength on the cylinder is the field strength outside the straight line and the distance r from the straight line: e*2 rh= h 0-->e= 2 0*r, where is the charge line density of the charged line.

In electrostatics, the relationship between the sum of the charges in the closed surface of the car and the integral of the electric flux generated by the electric field on the closed surface is demonstrated. Gauss's Law (Gauss'law) indicates the relationship between the charge distribution within the closed surface and the electric field generated.

Gauss's law is analogous to Ampere's law applied to magnetic fields in the case of electrostatic fields, both of which are concentrated in Maxwell's equations. Because of the mathematical similarity, Gauss's law can also be applied to other physical quantities determined by the inverse square law, such as gravitational force or irradiance.

The mathematical formula of Gauss's theorem is f·ds= (f)dv。Gauss's law shows the relationship between the charge distribution of a closed surface and the electric field generated. The void is a bounded closed area, the boundary of which is a segmented tape measure smooth closed surface.

Functions p(x,y,z), q(x,y,z). r(x,y,z) and their one-order partial derivatives are continuous on , where the positive side of is the outer side and cos, cos, and cos are the directional cosine of the outer normal vector of .

Gauss's theorem conceptGauss's theorem shows the relationship between the distribution of electric charges within a closed surface and the electric field generated. Gauss's theorem is analogous to the Gaussian law applied to magnetic fields in the case of electrostatic fields, both of which are concentrated in Maxwell's equations. Because of the mathematical similarity, Gauss's theorem can also be applied to other physical quantities determined by the inverse square law, such as gravitational force or irradiance.

The content of the theorem is set up in a bounded closed region of space, and its boundary is a sliced smooth closed surface.

Chinese name: Gauss's theorem.

English name: gauss

theorem

Definition: The flux through an arbitrary closed surface is equal to the algebraic sum of all charges enclosed by the closed surface as the ratio to the electric constant.

Applied disciplines: electric power (first-level discipline); General Theory (Secondary Discipline).