I understand that for a positive point charge at the origin, the resulting electric field extends out radially and has magnitude that decreases by $\frac{1}{r^2}$. However, I do not understand why the divergence (anywhere but the origin) is 0. If I imagine a point in space away from the origin, there are vectors on either side with different magnitudes. When thinking about this like a 'flow', I can't figure out how there is 0 divergence if the flow is decreasing.

I am even more confused when thinking about a field such as $\textbf{F}= x\hat{x}$. Many YouTube videos and textbooks state there is a positive divergence as the flow rate it increasing with $x$. So, why wouldn't the same logic apply for a flow rate decreasing by $1/r^2$ (negative divergence)?

Here is a picture which demonstrates my confusion (I know the field shown is not $\textbf{F}$)

Many thanks

I understand that for a positive point charge at the origin, the resulting electric field extends out radially and has magnitude that decreases by $\frac{1}{r^2}$. However, I do not understand why the divergence (anywhere but the origin) is 0. If I imagine a point in space away from the origin, there are vectors on either side with different magnitudes. When thinking about this like a 'flow', I can't figure out how there is 0 divergence if the flow is decreasing.

I am even more confused when thinking about a field such as $\textbf{F}= x\hat{x}$. Many YouTube videos and textbooks state there is a positive divergence as the flow rate it increasing with $x$. So, why wouldn't the same logic apply for a flow rate decreasing by $1/r^2$ (negative divergence)?

Here is a picture which demonstrates my confusion (I know the field shown is not $\textbf{F}$)