# No line or volume current density in Ampère's circuital law?

In Gauss's law we have continuous charge densities for lines, surfaces and volumes. However, regarding current density, Wikipedia, only have a surface current density. Don't we also have line and volume current densities for Ampère's circuital law?

The charge density that appears in Gauss's Law is a volume charge density.

The singular charge densities used in relation to Gauss's Law are mathematical models of volume charge densities for situations where the charge distribution has a small extent in one or more dimension. Everything in actual fact is a volume charge density. Similarly, every current density is a volume current density defined over a surface.

One could define current densities that have small extents in one or more dimension. However, the current density in Ampere's Law is a volume current density defined at a surface.

Current density and charge density are two different quantities. Charge density is defind for line, surface and volume but current density is defined as curret divided by area

However, regarding current density, Wikipedia, only have a surface current density. Don't we also have line and volume current densities for Ampère's circuital law?

The current density $\mathrm{J}$ is not a surface current density in that sense (line, surface, and volume charge densities are scalars while current density is a vector). That is, current density isn't the current density on a surface but rather through a surface normal to $\mathrm{J}$. It has units of $\mathrm{\frac{A}{m^2}}$ so that the flux of the current density through some surface gives the current through that surface.

In fact, there is a surface current density $\mathrm{K}$ (see, for example, Surface current and current density) which is used for currents confined to a surface and has units of $\mathrm{\frac{A}{m}}$ since, in this case, the 'surface' the current is through is a line.