What does divergence of electric field = 0 mean?

[15ongm]

Homework Statement

I just want to focus on the divergence outside the cylinder (r >R)

Homework Equations

The Attempt at a Solution

For r > R, I said ∇ * E = p/ε

But that's wrong. The answer is ∇ * E = 0

I'm confused because there is definitely an electric field outside the cylinder (r > R). The electric field points radially outwards and gets smaller the farther you get from the cylinder because

So I don't understand how the divergence of the electric field can be 0. I think the main part of my confusion is that I don't understand what the divergence is. I know how to mathematically compute the divergence but I don't understand it physically. Like when the divergence of the electric field is 0, what does that mean in terms of the physical electric field?

 

[TSny]

Gauss' law says that the divergence of E evaluated at some point equals the charge density at that same point divided by $\epsilon_0$.

These videos might help improve your conceptual understanding of divergence: