What does divergence of electric field = 0 mean?

Uj_K8p1Y-lcIn summary, the conversation discusses the calculation of the divergence of an electric field outside a cylinder with a charge distribution. The initial attempt was ∇ * E = p/ε, but the correct answer is ∇ * E = 0. The confusion arises from the existence of an electric field outside the cylinder, which points radially outwards and decreases with distance. The concept of divergence is also discussed, with the suggestion to watch videos for a better understanding. The explanation of Gauss' law is also mentioned as a helpful tool.
  • #1
15ongm
7
0

Homework Statement


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

Homework Equations


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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
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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?
 
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  • #2
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:
 

1. What is the meaning of divergence of electric field being 0?

The divergence of electric field being 0 means that the electric field is not spreading out or converging at a particular point in space. This indicates that the electric field is either constant or flowing in a closed loop.

2. Why is it important for the divergence of electric field to be 0?

It is important for the divergence of electric field to be 0 because it is a fundamental law of electromagnetism known as Gauss's Law. This law states that the electric flux through a closed surface is proportional to the total amount of electric charge enclosed within that surface. A non-zero divergence of electric field would violate this law.

3. Can the divergence of electric field be negative?

No, the divergence of electric field cannot be negative. Divergence is a measure of the net flow of a vector field out of a given point in space. Since electric field lines only originate from positive charges and terminate at negative charges, the divergence of electric field can only be positive or zero.

4. How is the divergence of electric field related to electric charge?

The divergence of electric field is directly related to the presence of electric charge. As mentioned earlier, Gauss's Law states that the electric flux through a closed surface is proportional to the total amount of electric charge enclosed within that surface. Therefore, the divergence of electric field being 0 indicates that there is no electric charge enclosed within the surface.

5. What are the practical applications of divergence of electric field being 0?

The practical applications of divergence of electric field being 0 include understanding the behavior of electric fields around conductors, insulators, and other materials. This knowledge is crucial in designing electrical systems, such as circuits, and in studying the behavior of electromagnetic waves.

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