Gauss theorem and the superposition principle

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2019-03-31 16:20:19

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The Gauss Theorem is one of the fundamental laws of electrodynamics, is structurally included in system of equations another great scientist – Maxwell. She expresses the connection between the threads of tension as electrostatic and electrodynamic fields passing through the surface closed type. The name of Carl Gauss sound in the scientific world is no less loud than, for example, of Archimedes, Newton or University. In physics, astronomy, and mathematics, you can find not so many areas, the development of which in a very direct way not promote this brilliant German scientist.

Gauss Theorem

The Gauss Theorem has played a key role in the study and understanding of the nature of electromagnetism. By and large it became a kind of generalization, and to some extent the interpretation of the famous Coulomb's law. This is the case, is not so rare in science, where the same phenomena can be described and formulated in different ways. But Gauss's theorem not only gained practical significance and practical application, she helped us to look at the known laws of nature in a somewhat different context.

In some ways it contributed to a big breakthrough in science, laid the Foundation of modern knowledge in the field of electromagnetism. So what is Gauss theorem and what is its practical application? If you take a pair of static point charges, approached to him particle to attract or repel with a force which is equal to the algebraic sum of all elements of the system. The total tension field formed as a result of this interaction will be the sum of its individual components. This ratio is widely known as the superposition principle allows to describe any system designed to push and pull charges, regardless of their total number.

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Gauss Theorem for a magnetic field

However, when such particles are very many scientists at first, in the calculations there were certain difficulties that cannot be resolved by application of the Coulomb law. To overcome them helped the Gauss theorem for a magnetic field, which, however, is fair for any power system charges, with decreasing tension, 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 full thread tension equal the sum of the electric potential of each point of this plane. The principles of interaction between elements are not taken into account, which greatly simplifies calculations. Thus, this theorem allows us to calculate the field even with an infinite number of carriers of electric charge.

the Theorem of Gauss for dielectrics

However, in reality, this is feasible only in some cases, their symmetrical arrangement, when there is a convenient surface through which it's easy to calculate force and tension of the thread. For example, a test charge placed inside a conducting shaped bodies will not have the slightest force action, as the indicator of the intensity of the field there is zero. The ability of the conductors to push it out electrically various fields is explained solely by the presence of charge carriers. In metals are electrons. These features are now widely used in the technique for creation of different spatial regions with no electric field. These phenomena well explain the theorem of Gauss for dielectrics, whose influence on the system of elementary particles is reduced to a polarization of their charges.

To create such effects, enough to surround a region of intensity metal shielding mesh. So protect against the effects of electrical field sensitive high-precision equipment and people.


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Alin Trodden - author of the article, editor
"Hi, I'm Alin Trodden. I write texts, read books, and look for impressions. And I'm not bad at telling you about it. I am always happy to participate in interesting projects."

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