Physical Motivation for Curl and Divergence

In summary, the conversation was about the concept of curl and divergence and the speaker's desire to build a better understanding of these fundamental operators. They mentioned their current understanding of curl as being similar to a paddle wheel spinning in a direction dependent on the vector field, while divergence is seen as the amount of "stuff" leaving in a specific direction. The speaker expressed a need for help and suggested looking at Wikipedia for explanations and translations in other languages.
  • #1
ninevolt
21
0
So I know what they are and I've been given some really vague and weak interpretations, but I want to build up my intuition and know more about the specifics of curl and divergence. To my understanding now I know that

curl is similar to a paddle wheel spinning in a direction dependent on the vector field, if the vector field lines are water currents.

Divergence is the amount of stuff leaving directed along the normal


So as you can see my understanding of these fundamental operators is crap, and I need a lot of help. Tips on how you interpret curl and rigorous definitions welcome (everything welcome)
 
Physics news on Phys.org
  • #2
I find the explanations on Wikipedia not so bad. You can also look at the pages in other languages and let Google translate them for you, so you will find a variety of different wordings.

Roughly speaking is the curl the rotation of a vector field and divergence measures attractors and repellers or the absence of them.
 

1. What is the physical significance of curl and divergence?

The curl and divergence are two important mathematical operations used in vector calculus to describe the behavior of vector fields in three-dimensional space. They are used to quantify the rate of change and the flow of a vector field at a given point.

2. How do curl and divergence relate to fluid flow?

In fluid dynamics, the curl of a vector field represents the rotation or circulation of the fluid at a given point, while the divergence represents the expansion or compression of the fluid. These properties are important in understanding the behavior of fluids in various applications such as aerodynamics and hydrodynamics.

3. What is the physical meaning of a curl-free vector field?

A curl-free vector field, also known as an irrotational field, has a curl of zero at every point. This means that the field is not rotating or curling in any direction. In physical terms, this can represent a conservative force, such as gravity, where the work done along a closed path is independent of the path taken.

4. How is divergence related to the concept of a source or a sink?

In vector calculus, a divergence-free vector field represents a field in which the flow of the field is equal in and out of a given region. This can be interpreted as a source or a sink, where the field is either generating or absorbing the values at a particular point.

5. Why is understanding curl and divergence important in physics?

Curl and divergence are essential concepts in physics as they help describe complex physical phenomena, such as fluid flow, electromagnetism, and heat transfer. They provide a quantitative way to analyze and understand the behavior of vector fields in three-dimensional space, making them valuable tools for scientists and engineers in a wide range of fields.

Similar threads

I Vector field and Helmholtz Theorem
    • Calculus
Replies
20
Views
3K
I What do Stokes' and Green's theorems represent?
    • Calculus
Replies
7
Views
1K
I Solve Vector Equation: iy + jx & (i + j)/√2
    • Calculus
Replies
3
Views
2K
Help with intuition of divergence, gradient, and curl
    • Calculus
Replies
8
Views
3K
I A one dimensional example of divergence: Mystery
    • Calculus
Replies
2
Views
2K
Understanding the Confusing Curl in R2 and R3: An Intuitive Explanation
    • Calculus
Replies
2
Views
3K
Div and curl in other coordinate systems
    • Calculus
Replies
2
Views
1K
I Do 4-divergences affect the eqs of motion for nth order perturbed fields?
    • Calculus
Replies
1
Views
1K
Intuitively understanding div(curl F) = 0
    • Calculus
Replies
4
Views
15K
A ZERO Curl and a ZERO divergence
    • Calculus
Replies
4
Views
8K

Hot Threads

Recent Insights

Back
Top