Ampère's law relates the integrated magnetic field around a closed loop to the electric current passing through the loop.In 1820, after Ørsted's experiment, André-Marie Ampère developed a theory of current interaction within a week. He deduced that the circulation of the magnetic field along any closed path equals the current passing through the loop (multiplied by the constant μ0). Analogy: the stronger the traffic flow on a ring road, the more powerful the air vortex above it, and the wind swirls along the roadside. Later, Maxwell generalized the law, adding the displacement current.
In 1820, Hans Christian Ørsted noticed that a current-carrying wire deflects a magnetic needle. André-Marie Ampère, inspired by this, presented a report with a quantitative law just a week later. In 1861, James Clerk Maxwell included the law in his equations and added the displacement current, correcting a contradiction with charge conservation.
The law is actively used to calculate magnetic fields in symmetric configurations: straight wire, solenoid, toroid. Limits of applicability: only for steady currents; when electric fields change over time, the displacement current must be considered. In the presence of magnetic materials, the relationship becomes more complex.
Calculation of magnetic fields in electric motors, generators, and transformers, design of MRI magnets.
Using Ampere's law, one can 'weigh' the current — with a current balance, the ampere is determined with high accuracy.
| \langle S_z \rangle | variable | Expectation value of the spin angular momentum along the quantization axis — spin angular momentum |
| C | variable | Normalization constant depending on the number of holes in the 3d band |
| R | variable | Radial dipole matrix element ratio |
| \mu_+ | variable | X-ray absorption coefficient for right circular polarization — absorption coefficient metre per kilogram |
| \mu_- | variable | X-ray absorption coefficient for left circular polarization — absorption coefficient metre per kilogram |
| E | variable | Photon energy — energy joule |
| \int_{L_3} | operator | Integration over the L3 absorption edge energy range — integral operator |


