What does it mean for a $2$ dimensional object to be charged with a charge distribution which is $1$ dimensional $\lambda$?

Question

I saw an example, in a tutorial of my Physics $2$ course that there was a hollow cylinder (which is $2$ dimensional) charged with uniform charge distribution $\lambda>0$ per unit length.

What does this mean? I thought that $2$ dimensional objects are suppose to be charge with surface charge density.

Isn't the length of such an object is infinity? (The area is of course finite, but the length of each circle is $2\pi R$ and there are infinite amount of circles.)

If this is the case then $$Q=\lambda l=\lambda\infty$$ and so the cylinder have an infinite amount of charge on it, which can't be true.

The TA was asked about it in class, but I wasn't able to understand his explanation (this was a video recitation filmed a few years back, and so I can't ask the TA), I have also seen it on an exam question, so I do think that whoever wrote that its a distribution $\lambda$ and not surface distribution $\sigma$ meant to write it.

Why is my analysis that $Q=\infty$ is incorrect, and what does it mean that the cylinder charged with uniform charge distribution $\lambda$?

Answer 1

I think it means that if we pick a section of the cylinder that is of length $l$, the charge on that section is $\lambda l$. Note that here length is measured with respect to the symmetry axis of the cylinder, ie, it is the length we normally refer to when talking about, say, a section of pipe 4m long.

Since a section of pipe that has length $l$ has surface area $2\pi R l$ and charge $\lambda l$, the surface charge density must be $\frac{\lambda}{2\pi R}$.