What Happens to Divergence When Field Lines Change Length?

[DunWorry]

Hey guys!

So I've been trying to get my head around Divergence of a vector field. I do get the general idea, however I thought of a hypothetical situation I can't get my head around. Look at the second vector field on this page, http://mathinsight.org/divergence_idea

it has a negative divergence. It makes sense because if you take a circular surface and measure the flux, there is more flux going into the sphere then going out. Also you can see as a whole the field is compressing towards the origin. However what happens if you take the same vector field, but the field lines are shorter on the outside and get longer towards the origin?

This means if I take a surface and measure the flux, more flux is going out than in because the field lines are longer towards the origin. This suggests a positive divergence, however looking at the field as a whole its clear the field is compressing towards the origin at an accelerating rate so the divergence should be negative?

Thanks!

 

[Khashishi]

In your case, the divergence would be positive at the surface and negative at the center. The divergence doesn't have to have the same value everywhere.