April 30, 2026 - In classical electromagnetism, Ampère's circuital law, often simply called Ampère's law, and sometimes Oersted's law, relates the circulation of a magnetic field around a closed loop to the electric current passing through that loop. The law was inspired by Hans Christian Ørsted's 1820 discovery ...

The magnetic field in space around an electric current is proportional to the electric current which serves as its source, just as the electric field in space is proportional to the charge which serves as its source. Ampere's Law states that for any closed loop path, the sum of the length elements ...

March 28, 2024 - This is different from Gauss’ Law, where the integral is over a closed surface (not a closed path, as it is here). In the context of Gauss’ Law, we refer to “calculating the flux of the electric field through a closed surface”; in the context of Ampere’s Law, we refer to “calculating the circulation of the magnetic field along a closed path”.

Ampere's Law is used to find the magnetic field generated by currents in highly symmetric geometries like the infinitely long wire and the solenoid. It is shown how magnetism can be used to convert macroscopic mechanical energy to do microscopic electrical work.

April 14, 2015 - Ampere's Law states that the magnetic field created by an electric current is proportional to that current's size.

June 15, 2026 - Ampère’s law, one of the basic relations between electricity and magnetism, stating quantitatively the relation of a magnetic field to the electric current or changing electric field that produces it.

April 2, 2026 - Ampère’s Law is the magnetic counterpart of Gauss’s Law for electricity: instead of a closed surface integral, it uses a closed line integral, and instead of relating the integral to enclosed charge, it relates the integral to enclosed current. Choosing the right closed path (the “Ampèrian loop”) transforms a potentially difficult integral into a one-step multiplication.

October 6, 2016 - This result is similar to how Gauss’s law for electrical charges behaves inside a uniform charge distribution, except that Gauss’s law for electrical charges has a uniform volume distribution of charge, whereas Ampère’s law here has a uniform area of current distribution.

One of Maxwell's equations, Ampère's law, relates the curl of the magnetic field to the current density and is particularly useful for current distributions with high degrees of symmetry.

Ampere’s law for static magnetic fields states that the magnetic field’s integral around closed contour is equal to the current enclosed by the contour.

the field inside, we use Ampère’s law along the path

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The figures below illustrate Gauss’s laws for the electric and magnetic fields in the context of an electric ... The circulation integral of the magnetic field ⃗B around any closed curve (loop) C is equal to the net electric ... Note: Only the component of ⃗B tangential to the loop contributes to the integral. The positive current direction through the loop is determined by the right-hand rule. ... The line integrals H ⃗B · d⃗s along the three Amperian loops are as indicated.

Ampere's Law.

July 20, 2017 - Use Ampere's law to calculate the magnetic field around a current loop.

As with Gauss's law, to use Ampere's law we depend on the symmetry of the configuration to make the needed simplifications to the calculations. Once we have expressions for fields from current carrying wires, we can investigate interactions between wires.