Understanding Divergence: Unit Vectors & Magnitude

[salman213]

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

 

[tiny-tim]

Hi salman213!

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.