and this equation is now the equivalent form of Maxwell’s equations; that is, instead of solving Maxwell’s equations for the
magnetic field intensity and the electric field intensity, we can solve for the magnetic vector potential and then obtain the
magnetic and electric field intensities as well as flux densities from the magnetic vector potential.
The relation in Eq. (11.49) is called the Lorenz condition or the Lorenz gauge. There are three questions associated with
Eqs. (11.49) and (11.50). First, is the Lorenz gauge the only possible choice? Second, how do we know that this choice is
correct? Third, why should we use the magnetic vector potential in the first place since we can obtain a second-order
equation in terms of H or E, as will be shown shortly? The answer to the first question is no. There are other choices that may
be used, but this particular choice eliminates the scalar potential in the equation and therefore simplifies the equation which,
in turn, also should simplify its solution. A commonly used gauge, particularly in static applications, is ∇J ¼ 0, which is
called the Coulomb’s gauge and was introduced in Chapter 8 [Eqs. (8.37) and (8.38)]. The answer to the second question is
that this choice is “consistent with the field equations.” The latter statement means that Lorenz’s condition is consistent with
the principle of conservation of charge. The answer to the third question is twofold: First, it allows representation in terms of
a single field variable A, instead of the need for E and H. Second, and perhaps more important, the magnetic vector potential
is sometimes more convenient to use than the electric field intensity E or the magnetic field intensity H. While it is not the
purpose here to prove this, it should be noticed that the magnetic vector potential is always in the direction of the current
density J. This means that if the current density has a single component in space, the magnetic vector potential also has a
single component. On the other hand, the magnetic field intensity has two components (perpendicular to the current).
Without actually solving the equations, it is intuitively understood that solving for a single component of a field in space
should be easier than solving for two components.