In introducing the dirac-delta function, my electrodynamics discusses the following function:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]v = 1 / r^2[/tex]r

The text states that "at every location, v is directed radially outward; if there ever was a function that ought to have a large positive divergence, this is it. And yet, when you actually calculate the divergence (using Eq. 1.71), you get precisely zero."

At least on the positive portion of the x-y-z axis, it seems to me that v would have a negative divergence, meaning that as you move away from the origin, the magnitude of the vectors (which all point radially outward from the origin), would get smaller. That is, for every point other than the origin, the amount going in would exceed the amount coming out (the definition of a sink). For example:

Origin---------->-------->------>---->-->

Does this not indicate a negative divergence?

This question has caused me to wonder if my understanding of the divergence function is flawed.

Any help is greatly appreciated,

--Brian

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# Dirac-Delta Function

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