What is the scope of application of Gauss s theorem, and under what conditions is Gauss s theorem us

Gauss's theorem. Suitable for any electrostatic field.

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 Ampère's law applied to magnetic fields in the case of electrostatic fields, and both are concentrated in Maxwell's equations.

Middle. Because of the mathematical similarity, Gauss's law can also be applied to other physical quantities determined by the inverse square law.

For example, gravity or irradiance.

Applicable to mathematics, electricity, etc. Since magnetic field lines always close the curve, any magnetic field line that enters a closed surface must come out of the surface, otherwise the magnetic field line will not close. 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 electric fields, so it is also called Gauss's theorem compared to Gauss's theorem in electrostatic fields, and the two are fundamentally different.

In the electrostatic field, because there are independent charges in nature, the electric field lines have a beginning and an end point, as long as there is a net residual positive (or negative) charge in the closed surface, the electric flux through the closed surface is not equal to zero, that is, the electrostatic field is an active field; In the magnetic field, since there is no separate magnetic pole in nature, the n pole and the s pole cannot be separated, and the magnetic inductance lines are closed lines without head and tail, so the magnetic flux through any closed surface must be equal to zero. Wish.

Whether inside or outside the sphere, the electric field strength is spherically symmetrical, and the Gaussian surface is taken as the sphere with radius r. Let r

Gauss's theorem, one of the fundamental equations for the electrostatic field, which gives the relationship between the area component of the electric field strength on any closed surface and the total amount of electricity enclosed within the closed surface.

The flux through an arbitrary closed surface is equal to the algebraic sum of all charges enclosed by the closed surface to the ratio of the electric constant. Applied disciplines: electric power (first-level discipline); General Theory (Secondary Discipline).

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 surrounded 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 and late to close. 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 electric fields, so it is also called Gauss's theorem.

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.