Magnetic vector potential

The magnetic vector potential is a vector field whose curl equals the magnetic field. It can describe magnetic effects even in regions where the magnetic field is zero.

Magnetic field: A physical field that exerts magnetic forces on moving charges and magnetic materials. The curl of the vector potential gives this field.
Aharonov–Bohm effect: A quantum phenomenon in which electromagnetic potentials affect particle interference where the corresponding fields vanish. It demonstrates an observable role for the potential outside regions containing magnetic field.
Vector field: A function assigning a vector to each point in a space. The magnetic vector potential assigns a vector throughout space.
Magnetic scalar potential: A scalar function whose negative gradient represents a magnetic field in regions without electric currents. It can replace a vector potential locally where currents are absent.
Gauge transformation: A change in mathematical fields that leaves observable physical quantities unchanged. Adding a gradient to the potential leaves its magnetic field unchanged.
Magnetic dipole moment: A vector quantity measuring the strength and orientation of a magnetic dipole. The potential generated by a localized magnetic dipole has a characteristic spatial form.
Curl: A vector differential operator measuring the local rotation of a vector field. Taking the curl of the potential produces the magnetic field.
Electric scalar potential: A scalar field whose spatial variation contributes to the electric field. It is the scalar partner of the vector potential in electromagnetic descriptions.
Coulomb gauge: A gauge condition in which the divergence of the electromagnetic vector potential is zero. This common choice simplifies equations for the magnetic potential.
Biot–Savart law: A law giving the magnetic field produced by steady electric currents. Integrating its field relation can yield the vector potential of a current distribution.

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