Why is it that when calculating the electric field of a cylinder, the linear charge density is used? I think that the surface charge density is more appropriate as the cylinder, unlike a rod, does have a surface. However if I look at textbooks like Halliday or even stuff on the internet it seems everyone uses the linear charge density. Why is it so?

Example photos

 A: People use the linear density because it is equivalent.

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*If we consider a cylinder of radius $R$ with surface charge $\sigma$, then to calculate the electric field outside $(r>R)$ we apply Gauss' law choosing a cylinder of length $L$ as our Gaussian surface:
$$\iint\vec{E}\cdot\vec{dS}=\frac{(2\pi RL)\sigma}{\varepsilon_0}$$
and we get
$$\vec{E}=\frac{R\sigma}{r\varepsilon_0}\hat{r}$$

*Notice that this is the electric field that a linear density of value $\lambda=2\pi R\sigma$ would create if it were located at the center of the cylinder $(r=0)$. So this is saying us that we have an equivalence (a purely operational one); every time we want to calculate the field created by a (constant) charge $\sigma$ located at the surface of a cylinder we can just forget about the cylinder and replace it with a line of charge $\lambda=2\pi R\sigma$. The field created by the surface and the one by the line are the same in the region of interest.

*Notice finally, that the equivalence is something that we can expect by physical considerations. Consider the cylinder first. What charge is there in a given portion of length $L$? Well,
$$Q=\underbrace{(2\pi RL)}_{\rm surface}\sigma$$
or per unit length
$$\frac{Q}{L}=2\pi R\sigma.$$
So if the charge in the cylinder per unit length is $2\pi R\sigma$, it makes sense (physically) to put $\lambda=2\pi R\sigma$.

A: Usually, for simplicity, the cylinder is assumed to be infinite (practically the length is much greater than the radius), so that charge on the cylinder is much larger.
In order to tackle this, the term charge per unit length $(\lambda)$ is used which remains constant for uniform charge distribution and is more convenient.
