# What does it intuitively mean that the divergence of a vector field is 0?

I was going through an Electrodynamics textbook, and as a prerequisite it requires elemenets of Vector calculus and Multivariable calculus. They discussed divergence, and gave examples of fields with positive and negative divergence. And they also gave a graphic example of a vector field where all the vectors are equal and parallel to each other as a field with 0 divergence.

However, to me it seems that this should have a positive divergence, not 0. Can someone explain this to me?

• Check out the divergence theorem on Wikipedia and if you still don't understand look at The Feynman Lectures Vol. 1 I believe. – Tom Copeland Sep 4 '12 at 6:53
• rather The Feynman Lectures on Physics Vol. II. – Tom Copeland Sep 4 '12 at 7:18

• Pleas also note the "Divergence Theorem" as a special case of Stoke's theorem: en.wikipedia.org/wiki/Divergence_theorem for some intuition. A nice example is found population dynamics. Suppose you want to measure the change of population in your country (immigration, emigration) in a simplified example (without birth/death rates). Then you could either look at the integral of the divergence of your vector field $F$ (it denotes where people move) in the country or you could integrate $F$ along the border (surface). If $F$ has divergence $0$ you have no net in/outflows in the country... – vanguard2k Sep 4 '12 at 6:53