Why is charge density dependent on distance?

Question

If we suppose that we want to find the electric field at some point P. Let's consider a small volume element $ \Delta V_i$ , which contains an amount of charge $\Delta q_i$. The distance between charges within the volume element $\Delta V_i$ are much smaller than compared to $r$, the distance between $ \Delta V_i$ and $P$. So, the volume charge density $\rho(\vec r)$ as: $$\rho(\vec r)= \frac{dq}{dV}$$

This is the definition given for Volume Density Charge. Why is $\rho(\vec r)$ a function of $\vec r$ ?

Answer 1

It becomes quite evident when you draw a figure and label the vectors involved.

When we define the charge density $\rho$, what we are defining is $\rho(r’)$. And if you want to find field at point $P$, we can rewrite it as $\rho(r-R)$. Now you can see why it’ll depend on $r$.

Answer 2

$\rho$ is dependent on r because it describes the charge density in all of space.

Looks like the author of this text is using r for two purposes. An parameter for $\rho$ and one to descripe a point P in reasonable distance to the charges.