I am studying a course in Electrodynamics and we are just covering retarded potentials and the Hertzian dipole.
In my lecture notes, we have calculated the magnetic vector potential $A$ in the Lorenz gauge as $$A = \frac{\mu_0}{4 \pi r} [\ddot{p}]$$ where the square brackets indicated evaluated at the retarded time.
Now the confusion comes in once we start to compute the fields $B$ and $E$.
Calculation of $B$ is easy enough using $B = \nabla \times A$, but for $E$ we are using $$\frac{1}{c^2} \frac{\partial E}{\partial t} = \nabla \times B$$ but where has the $\mu_0 j$ gone from this equation (Ampere's law??)?? I don't know if it has anything to do with the fact we are neglected terms in $\frac{1}{r^2}$ and higher, but I am quite confused about where this equation has come from.
Any insight would be appreciated