How do you classify current density?

Question

When talking about the electromagnetic field one usually thinks of:

• the electric field described locally by its intensity $\vec{E}$ and its flux density $\vec{D}$,
• the magnetic field described locally by its intensity $\vec{H}$ and its flux density $\vec{B}$.

There is however a fifth quantity: the electric current density $\vec{J}$. The first four quantities live together in pairs with each pair having its own designation. Poor little $\vec{J}$ seems to be all alone (no family) even though it has good ties with its friends: \begin{equation} \vec{J}=\sigma\vec{E} \end{equation} \begin{equation} \text{curl} \, \vec{H} = \vec{J} + \frac{\partial \vec{D}}{\partial t} \end{equation}

My question is: In which category should we place $\vec{J}$? If $\vec{E}$ and $\vec{D}$ are electric and $\vec{H}$ and $\vec{B}$ are magnetic, what is $\vec{J}$?

It's obviously neither electric nor magnetic. Or maybe it's both. Is there an already established terminology for the field which "contains" $\vec{J}$?

Answer 1

You are forgetting of a major part of the story, the charge density $\rho$. The fields you are talking about, namely $\vec{E},\vec{D},\vec{B}$ and $\vec{H}$, are consequences of the configuration of electric sources in classical electrodynamics. These sources are the charge density $\rho$, and the current density $\vec{J}$, and both are electrical in nature, since they specify the configuration of electric charges and electric currents.