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counter-intuitive divergence

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/0:
Given the function



We have , and yet, at www.pierce.ctc.edu/dlippman/g1/fullgrapher3d.html, the field is clearly diverging away from the origin AND slowing down.

Why is this?

zzdfa:
copying from wikipedia:

--- Quote ---More rigorously, the divergence is defined as derivative of the net flow of the vector field across the surface of a small region relative to the volume of that region. Formally,

(Image removed from quote.)
--- End quote ---

so if you take smaller and smaller spheres around the centre, i guess the flux across the surface of the sphere gets smaller faster than the volume of the sphere shrinks. hence the ratio tends to 0.

just to clarify; divV=0 only at the origin, right?

/0:
Yeah it seems like divF = 0 everywhere...
I dfon't know if divF is defined at the origin...

zzdfa:
Intuitive explanation:
this is just gauss' law.
take any closed surface not containing the origin in that space (i am pretty sure divF is undefined at 0, maybe not; i cbf doing the calculations); any arrows going into it (flux) is balanced by stuff going out of it. hence the flux is zero and using the definition above, div=0 as well.

/0:
But does it matter that the arrows get shorter as you go out? It's like if you have a closed gaussian surface, the field lines will be stronger at one side than the other

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