Ampère's circuital law

A Maxwell equation relating the magnetic field integrated around a closed path to the electric current and changing electric flux through a surface bounded by that path.

Maxwell–Ampère equation: A Maxwell equation stating that magnetic-field circulation is sourced by conduction current and changing electric displacement. This is the modern form of the law, including Maxwell’s displacement-current term.
Line integral: An integral that accumulates a scalar or vector quantity along a curve. The magnetic field is accumulated along the closed path in the law.
André-Marie Ampère: A French physicist whose experiments and theories helped establish electrodynamics. The circuital law bears his name and grew from his work on current and magnetism.
Ampèrian loop: A chosen closed path used to apply Ampère’s circuital law to a magnetic-field calculation. Its shape is selected to make the field integral simple for a symmetric source.
Biot–Savart law: A relation that calculates magnetic fields from steady current distributions. It gives the field directly, whereas Ampère’s law relates circulation to enclosed sources.
Ampère's law in differential form: The local equation relating the curl of the magnetic field to current density and the time derivative of electric displacement. It expresses the law at each point rather than around a closed path.
Closed curve: A curve whose endpoints coincide, forming a complete loop. It supplies the boundary along which magnetic circulation is evaluated.
James Clerk Maxwell: A Scottish physicist who formulated the classical theory of electromagnetism. He added displacement current to the law and incorporated it into Maxwell’s equations.
Magnetic field of a straight current-carrying wire: The magnetic field produced by a long straight wire carrying electric current. A circular path around the wire makes the law yield the field directly.
Gauss's law for magnetism: A Maxwell equation stating that the net magnetic flux through any closed surface is zero. It constrains magnetic flux, not circulation around a loop.

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