Help with Newtonian Potentials for Helmholtz Decomposition

[Savant13]

I'm trying to find a divergenceless vector field based on its curl, and discovered that I could use a http://en.wikipedia.org/wiki/Helmholtz_decomposition" , and the article I found on this didn't make much sense to me.

First, can someone confirm that the dimension referred to in the Newtonian potential article is the number of spatial dimensions in which the field exists? If not, what is it?

Next, the exponent on what appears to be the absolute value of x for more than two dimensions can only be negative, which doesn't make sense to me in the context of the problem I am working on. Also, is that an absolute value, or some other notation?

 

[HallsofIvy]

Yes, d is the number of spatial dimensions. If d= 3 then the "Newtonian potential" is (-1/(3(2-3)(4pi/3))|x|^-1= 1/(4pi|x|). Why would that "not make sense"? What problem are you working on?

 

[Savant13]

See the thread in the classical physics forum. I started this one because no one was responding to the other one.