Gauge fixing#Coulomb gauge

The Coulomb gauge (due to the relationship with the Coulomb potential ( see below); well Strahlungseichung or transverse gauge ) is a possible calibration of electrodynamics, thus describes a limitation of the electrodynamic potentials.

Gauge freedom of electrodynamics

To facilitate the solution of Maxwell's equations, one introduces for the electric and magnetic field, the scalar potential and the vector potential, the classically observable fields by

Describe.

This definition allows so-called gauge freedom in the choice of a scalar potential and vector potential, which have no effect on measurable quantities, especially on electric field and magnetic flux density.

The Coulomb gauge

Because of it and follow the recorded results in the next section.

( The gauge freedom here is that you can add to any rotational field, because the divergence of a vector of the form always results in zero. )

The inhomogeneous Maxwell equations in the Coulomb gauge

If, with this calibration, the potentials in the so-called inhomogeneous Maxwell equations ( the Gaussian law and the extended law of induction ) a, one obtains

The first equation is

Dissolved, that is, the scalar potential is identical to the Coulomb potential in this calibration.

The second equation is an inhomogeneous wave equation with the solution obtained by the method of the retarded potential:

The sustained-release time is given by. Physically, the last specified difference in the time it takes for a light or radar signal to travel from the starting point ( the point of integration ) to go through the route the signals to the arrival point.

In the use of two different times in the integral - the scalar potential, the vector potential t t ' - the main advantage and main disadvantage of the specified calibration. The competing Lorenz gauge has this disadvantage, but is explicitly invariant relativistic, by consistently taking into account the retardation.

If there are no sources ( charges and currents ) present, the equations simplify to

So the vector potential satisfies the homogeneous wave equation.