Starting with Equation 9–5 and substituting the constitutive equations:

(9–27)

This can be rearranged as:

(9–28)

Assuming a quasi-steady model (that is, neglecting transient terms)

(9–29)

Similarly for Equation 9–3:

(9–30)

Using the constitutive relation between the Magnetic Induction () and the Magnetic Field (), in addition to the quasi-steady approximation:

(9–31)

Using vector identities (Equation 9–22) assuming uniform magnetic permeability, and enforcing the Coulomb gauge that , the transport equation for the magnetic vector potential becomes:

(9–32)

Note that the left-hand side of the transport equation for the magnetic vector potential has only transport by diffusion, which is balanced by the sources on the right-hand side.