Vector Calculus: Question about the origin of the term 'divergence'

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SUMMARY

The term 'divergence' in vector calculus refers to the operation that measures the flux density of a vector field. When the divergence is positive, it indicates that the vector field spreads outward, while a negative divergence signifies convergence of field lines. The 'curl' operation, on the other hand, quantifies the rotational density of a vector field, with its magnitude reflecting the strength of rotation. Both operations are essential in understanding the behavior of vector fields in various applications, including electrodynamics.

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  • Understanding of vector calculus concepts
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  • Knowledge of electrodynamics principles
  • Basic grasp of differential operators
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  • Study the mathematical definition of divergence in vector calculus
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Vectronix
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Why is the divergence operation called the 'divergence?' What is the significance of this operation on a vector-valued function? And what about "the curl?" The curl seems self-explanatory (at least it does in electrodynamics), but I need someone to expound on 'the curl' as well.
 
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The divergence gives you flux density of a vector field. If it's positive in a region then the vector field spreads outward from itself. That's why it's called divergence.

And the curl is a sort of rotational density of a vector field. Curl is a vector whose magnitude is proportional to the strength of rotation of the vector field. Hence it's called curl.
 
what said:
The divergence gives you flux density of a vector field. If it's positive in a region then the vector field spreads outward from itself. That's why it's called divergence.

Hi what! Hi Vectronix! :smile:

And, conversely, if the divergence is negative, then the field lines converge. :wink:

In particular, you get divergence round sources, and convergence round sinks.
 

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