Understanding Divergence: Unit Vectors & Magnitude

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SUMMARY

The discussion centers on the concept of divergence in vector fields, specifically in relation to unit vectors and their magnitudes. Positive divergence occurs when the magnitude of vectors exiting a region exceeds those entering it. Conversely, when unit vectors are uniformly distributed in a circular formation, the divergence is zero, as the inflow equals the outflow. The conversation also highlights that zero divergence typically exists except at singularities, such as point charges in electric fields.

PREREQUISITES
  • Understanding of vector fields
  • Familiarity with the concept of divergence in calculus
  • Knowledge of unit vectors and their properties
  • Basic principles of electric fields and singularities
NEXT STEPS
  • Study the mathematical definition of divergence in vector calculus
  • Explore the implications of divergence in fluid dynamics
  • Learn about the role of divergence in electromagnetism, particularly Gauss's Law
  • Investigate the relationship between divergence and conservation laws in physics
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Students of mathematics and physics, particularly those studying vector calculus and electromagnetism, as well as educators seeking to clarify the concept of divergence in vector fields.

salman213
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1. I was just trying to understand what divergence means so I hope someone can help me out.

Well from what I have read if I take a vector field and use an infinitesimal region, if the vector going in is smaller than the vector going out there is positive divergence.

Does this mean if i make a circle with UNIT VECTORS there is ZERO divergence. Because `what is going in`, is the same as going out,

[URL][PLAIN]http://img11.imageshack.us/img11/9028/31455816et8.jpg


If they were NOT unit vectors or vector of the same magnitude then there Would be divergence? is that the correct concept?



Homework Equations





The Attempt at a Solution

 
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Hi salman213! :smile:

If you mean unit vectors all going out from a particular point, and a small circle round that point, then there is divergence, because all the vectors are going out of the circle.

Zero divergence means conservation of whatever-it-is …

often you have zero divergence everywhere except at "sources" and "sinks" …

eg an electric field with zero divergence except at the "singularities" where point charges are.
 

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