Exploring Divergence in Vector Calculus

In summary: Well, effectively you did by overwriting it. Perhaps you can restore the original ?Yes, I can. Thank you.
  • #1
Physgeek64
247
11
Got it. Thank you ;)
 
Last edited:
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  • #2
Hi there,

Looks a bit like homework, for which we have a nice template !

Is it allowed to simplify this exercise to a sphere with the origin at the center ? Because if it is about a cube with the origin way outside of the cube, things seem complicated to me...

In the simple case ##\vec r ## goes to ## \vec r'= {\rm \ ?} ## so that ## \vec h = \vec r'- \vec r = {\rm \ ?} ## and that you can subject to the divergence operation (from its definition) , I should hope ?
 
  • #3
BvU said:
Hi there,

Looks a bit like homework, for which we have a nice template !

Is it allowed to simplify this exercise to a sphere with the origin at the center ? Because if it is about a cube with the origin way outside of the cube, things seem complicated to me...

In the simple case ##\vec r ## goes to ## \vec r'= {\rm \ ?} ## so that ## \vec h = \vec r'- \vec r = {\rm \ ?} ## and that you can subject to the divergence operation (from its definition) , I should hope ?

Its okay, I have sorted out my queries. But thank you. I didn't know whether to post this in homework as it is not technically homework, as I am doing it a while in advance so I was hoping more for general background information than for specifics on how to do the question. :)
 
  • #4
Please don't delete the original post -- it makes the thread incomprehensible !

Was your answer ##3\alpha## ?

What kind of background info did you have in mind ?
 
  • #5
BvU said:
Please don't delete the original post -- it makes the thread incomprehensible !

Was your answer ##3\alpha## ?

What kind of background info did you have in mind ?
ahh I am sorry- I just don't know how to delete the post.
Kind of- I got the volume increase to be 1+divh, which is the same thing?
 
  • #6
Physgeek64 said:
ahh I am sorry- I just don't know how to delete the post.
Well, effectively you did by overwriting it. Perhaps you can restore the original ?

Kind of- I got the volume increase to be 1+divh, which is the same thing?
Relative, I assume. Sounds good. Can you underpin it ?
 

FAQ: Exploring Divergence in Vector Calculus

What is divergence?

Divergence is a mathematical operation that measures the flow of a vector field outwards from a given point. It is represented by the symbol "∇ ⋅" and is a key concept in vector calculus.

How is divergence different from curl?

While divergence measures the flow outwards from a point, curl measures the rotation of a vector field around that point. In other words, divergence represents the spreading or converging of a vector field, while curl represents the twisting or turning of a vector field. Both are important concepts in vector calculus and are closely related.

What are some real-life applications of divergence?

Divergence has numerous applications in physics and engineering, particularly in the fields of fluid dynamics and electromagnetism. For example, it is used to calculate the flow of fluids and the strength of electric and magnetic fields.

How is divergence calculated?

The divergence of a vector field is calculated using the partial derivatives of its components with respect to each coordinate. In other words, it is the sum of the rates of change of each component in the x, y, and z directions. This can be represented mathematically as "∇ ⋅ F = ∂F/∂x + ∂F/∂y + ∂F/∂z".

Can divergence be negative?

Yes, divergence can be negative. This indicates that the vector field is converging, or flowing inwards towards a point. If the divergence is positive, it means the vector field is spreading or flowing outwards from a point. A divergence of zero indicates that the vector field is neither spreading nor converging at that point.

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