Ампер айналымы заңы және электромагнетизм негіздері

Concept in classical electromagnetism

In classical electromagnetism, Ampère's circuital law (not to be confused with Ampère's force law) relates the circulation of a magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell derived it using hydrodynamics in his 1861 published paper "On Physical Lines of Force". In 1865 he generalized the equation to apply to time varying currents by adding the displacement current term, resulting in the modern form of the law, sometimes called the Ampère–Maxwell law, which is one of Maxwell's equations which form the basis of classical electromagnetism.

In 1820 Danish physicist Hans Christian Ørsted discovered that an electric current creates a magnetic field around it, when he noticed that the needle of a compass next to a wire carrying current turned so that the needle was perpendicular to the wire. He investigated and discovered the rules which govern the field around a straight current carrying wire:
The magnetic field lines encircle the current carrying wire. The magnetic field lines lie in a plane perpendicular to the wire. If the direction of the current is reversed, the direction of the magnetic field reverses. The strength of the field is directly proportional to the magnitude of the current. The strength of the field at any point is inversely proportional to the distance of the point from the wire. This sparked a great deal of research into the relation between electricity and magnetism. André Marie Ampère investigated the magnetic force between two current carrying wires, discovering Ampère's force law. In the 1850s Scottish mathematical physicist James Clerk Maxwell generalized these results and others into a single mathematical law. The original form of Maxwell's circuital law, which he derived as early as 1855 in his paper "On Faraday's Lines of Force" based on an analogy to hydrodynamics, relates magnetic fields to electric currents that produce them. It determines the magnetic field associated with a given current, or the current associated with a given magnetic field. The original circuital law only applies to a magnetostatic situation, to continuous steady currents flowing in a closed circuit. For systems with electric fields that change over time, the original law (as given in this section) must be modified to include a term known as Maxwell's correction (see below).

There are a number of ambiguities in the above definitions that require clarification and a choice of convention. First, three of these terms are associated with sign ambiguities: the line integral ∮C could go around the loop in either direction (clockwise or counterclockwise); the vector area d'S' could point in either of the two directions normal to the surface; and Ienc is the net current passing through the surface S, meaning the current passing through in one direction, minus the current in the other direction—but either direction could be chosen as positive. These ambiguities are resolved by the right hand rule: With the palm of the right hand toward the area of integration, and the index finger pointing along the direction of line integration, the outstretched thumb points in the direction that must be chosen for the vector area d'S'. Also the current passing in the same direction as d'S' must be counted as positive. The right hand grip rule can also be used to determine the signs. Second, there are infinitely many possible surfaces S that have the curve C as their border. (Imagine a soap film on a wire loop, which can be deformed by blowing on the film). Which of those surfaces is to be chosen? If the loop does not lie in a single plane, for example, there is no one obvious choice. The answer is that it does not matter: in the magnetostatic case, the current density is solenoidal (see next section), so the divergence theorem and continuity equation imply that the flux through any surface with boundary C, with the same sign convention, is the same. In practice, one usually chooses the most convenient surface (with the given boundary) to integrate over.