Homework Help: What does divergence of electric field = 0 mean?

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1. Apr 3, 2016

15ongm

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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?

2. Apr 3, 2016

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:

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