The Gauss theorem and the superposition principle

Gauss's theorem is one of the fundamental laws of electrodynamics, structurally included in the system of equations of another great scientist, Maxwell. It expresses the connection between the fluxes of tension of both electrostatic and electrodynamic fields passing through a surface of a closed type. The name of Karl Gauss sounds in the scientific world no less loudly than, for example, Archimedes, Newton or Lomonosov. In physics, astronomy and mathematics, not so many spheres can be found, to the development of which the most ingenious German scientist did not directly help.

Gauss's theorem played a key role in the study and understanding of the nature of electromagnetism. By and large, it has become a kind of generalization and, to some extent, an interpretation of Coulomb 's famous law. This is just the case, not so rare in science, when the same phenomena can be described and formulated in different ways. But Gauss's theorem not only acquired practical importance and practical application, it helped to look at the known laws of nature in a slightly different perspective.

In some ways, it contributed to a grand breakthrough in science, laying the foundation of modern knowledge in the field of electromagnetism. So what is the Gauss theorem and what is its practical application? If we take a pair of static point charges, the particle brought to them will be attracted or repelled with a force that is equal to the algebraic sum of the magnitudes of all the elements of the system. In this case, the tension of the total cumulative field formed as a result of such interaction will be the sum of its individual components. This relation has become widely known as the principle of superposition, which makes it possible to accurately describe any system created by multi-vector charges, regardless of their total number.

However, when there are a lot of such particles, scientists initially had certain difficulties in the calculations, which could not be resolved using the Coulomb law. To overcome them, the Gauss theorem for a magnetic field helped, which, however, is valid for any power systems of charges having a decreasing intensity proportional to r ^-2 . Its essence boils down to the fact that an arbitrary number of charges surrounded by a closed surface will have a total flux of intensity equal to the total value of the electric potential of each point of the given plane. In this case, the principles of interaction between elements in the calculation are not accepted, which greatly simplifies the calculation. Thus, this theorem makes it possible to calculate the field even with an infinite number of charge carriers.

True, in reality this is feasible only in some cases of their symmetrical arrangement, when there is a convenient surface through which the strength and intensity of the flow can be easily calculated. For example, a test charge placed inside a spherical conductive body will not experience the slightest force, since the field strength is zero. The ability of the conductors to push out the various electrically fields is explained solely by the presence of charge carriers in them. In metals, this function is performed by electrons. Such features are now widely used in engineering to create various spatial regions in which electric fields do not act. These phenomena perfectly explain the Gauss theorem for dielectrics, whose influence on the systems of elementary particles reduces to the polarization of their charges.

To create such effects, it is enough to surround a certain area of tension with a metallic screening grid. So, sensitive high-precision devices and people are protected from the impact of electric fields.