Purcell Electromagnetism p.301-303: "the longitudinal current I flows, in effect, on the cylinder itself"?

[Rob2024]

Homework Statement

I quote "As for the field inside the solenoid, the longitudinal current
I flows, in effect, on the cylinder itself. Such a current distribution, a
uniform hollow tube of current, produces zero field inside the cylinder and the fact that a circular path inside the tube encloses
no current), leaving unmodified the interior field we calculated before. If
you follow a looping field line from inside to outside to inside again,
you will discover that it does not close on itself. Field lines generally
don’t. You might find it interesting to figure out how this picture would be changed if the wire that leads the current I away from the coil were
brought down along the axis of the coil to emerge at the bottom."

Relevant Equations

N/A

I don't understand what the book meant as 'longitudinal current'. Is this in the axial direction (z direction) or the azimuthal direction (\phi direction)? It would only make sense if the current is in the axial direction. A confirmation of my guess would be appreciated. A picture from the book is attached.

 

[kuruman]

Longitudinal is the direction along the z-axis of the cylinder as you surmised.