Electric and magnetic potentials

Coulomb gauge

The Coulomb gauge of the magnetic potential is defined by the gauge fixing condition

Proof of gauge validity

Let and let solve Poisson’s equation

i.e. where is the Green’s function for the Laplacian. Then letting we have and

as required.

The main advantage of this gauge is that Ampère’s circuital law is simplified using

see e.g. Magnetostatics MOC.

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