The electromagnetism for forms

Question

Let $(M,g)$ be a riemannian manifold, $F\in \Lambda^2$ and $j,j' \in \Lambda^1$. The electromagnetic equations for forms are:
$$ dF=j'\wedge F$$
$$d^* F=j$$
If $j'=0$, we have the Maxwell equations.
Have these equations a physical meaning?

Comments

They have physical meaning if $j$ is a known function of $x$ and $F$ is unknown function (field).

Generally if some equations have physical solutions, they themselves are physical.

Answer 1

We could add $d^* j=0$ and $dj'=0$.