law

Ampere's law

Ampère's law relates the integrated magnetic field around a closed loop to the electric current passing through the loop.
11 related articles · 1 formulas · 1 who worked here

Description

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.

History

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.

How it works

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.

In practice

Calculation of magnetic fields in electric motors, generators, and transformers, design of MRI magnets.

Fun fact

Using Ampere's law, one can 'weigh' the current — with a current balance, the ampere is determined with high accuracy.

Concept graph →

Formulas

$$\langle S_z \rangle = \frac{C}{R} \int_{L_3} (\mu_+ - \mu_-) dE$$
The spin magnetic moment relates to the L3-edge XMCD integral.
What is in the formula
\langle S_z \ranglevariableExpectation value of the spin angular momentum along the quantization axis — spin angular momentum
CvariableNormalization constant depending on the number of holes in the 3d band
RvariableRadial dipole matrix element ratio
\mu_+variableX-ray absorption coefficient for right circular polarization — absorption coefficient metre per kilogram
\mu_-variableX-ray absorption coefficient for left circular polarization — absorption coefficient metre per kilogram
EvariablePhoton energy — energy joule
\int_{L_3}operatorIntegration over the L3 absorption edge energy range — integral operator
$\langles_z\rangle\approx\frac{1}{r}\int_{l_3}(μ_+-μ_-)de$ · 2607.11058

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