What do curl/Dovergence of various fields represent?

  • Thread starter swraman
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In summary, the symbols Div and Curl in the given conversation represent measures of sources and sinks and rotation in a field, respectively. The fields being discussed are gravitational, electric, and magnetic, and they are considered conservative in physics. The exact correlations between these fields are still unknown and may require further study.
  • #1
swraman
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jsut wondering, is there any realistic OR theoretical significance to:

[tex]Div \stackrel{\rightarrow}{G}[/tex]
[tex]Div \stackrel{\rightarrow}{E}[/tex]
[tex]Div \stackrel{\rightarrow}{B}[/tex]
[tex]Curl \stackrel{\rightarrow}{G}[/tex]
[tex]Curl \stackrel{\rightarrow}{E}[/tex]
[tex]Curl \stackrel{\rightarrow}{B}[/tex]

where [tex]\stackrel{\rightarrow}{G}[/tex], [tex]\stackrel{\rightarrow}{E}[/tex] and [tex] \stackrel{\rightarrow}{B}[/tex] are a gravitational, electric, and magnetic field respectivley.

Thanks
 
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  • #2
Looks like a homework question. What do you think the answers are? You need to make an attempt.
 
  • #3
Loosely speaking, 'divergence' is a measure of the sources and sinks to a field. 'Curl' is a measure of the rotation.
 
  • #4
No, it is not a homework question. I am just studying for finals and I have calculus and physics left...so a lot of these kind of questions have been going through my head. We talked a little about it in math, something to do with the field being conservative (havent gotten that far in my studying yet).
And from physics gravitational and electrical fields are conservative...but I just don't know what the exact correlations between the 2 are and was wondering if there was one.
 
  • #5
i wish someone would've helped me with this, it showed up on the final I was studying for. =\
 
  • #6
swraman said:
i wish someone would've helped me with this, it showed up on the final I was studying for. =\

Homework/coursework style questions should be placed in the homework forums.

Next time post your question in the correct forum, and you are more likely to receive help. However, you must make an effort: we don't just answer such questions for students.
 

1. What is the difference between curl and divergence?

Curl and divergence are both mathematical operations used to represent the behavior of vector fields. However, they have different interpretations and implications. Curl measures the rotation or circulation of a vector field, while divergence measures the expansion or convergence of a vector field.

2. How is curl represented mathematically?

Curl is mathematically represented as the vector cross product of the del operator (∇) with the vector field. It is written as ∇ x F, where F is the vector field.

3. What does a positive or negative curl value indicate?

A positive curl value indicates a counterclockwise rotation or circulation of the vector field, while a negative value indicates a clockwise rotation or circulation. A curl value of zero indicates that the vector field is irrotational, meaning there is no rotation or circulation.

4. How is divergence represented mathematically?

Divergence is mathematically represented as the dot product of the del operator (∇) with the vector field. It is written as ∇ ⋅ F, where F is the vector field.

5. What is the physical significance of divergence?

Divergence represents the flow of a vector field from a particular point. A positive divergence value indicates that the vector field is expanding outward from the point, while a negative value indicates that the vector field is converging inward towards the point. A divergence value of zero indicates that the vector field is incompressible, meaning there is no flow in or out of the point.

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