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1) it introduces the dirac delta function in dimension 1

δ(X) = 0 if x≠0 and δ(x)= ∞ if x= 0 and

∫δ(x)dx = 1

it then states div(

**r**/r^3) = 4∏δ(X)

the justification is from the divergence theorem, if we take the surface integral around

**r**/r^3 the result is 4 pi while the divergence is zero everywhere except at the origin. i find two problems with this argument, one, the proof for the divergence theorem given in elementary calculus assumes the function is continuously differentiable, which is not the case with the inverse squared field, hence the divergence theorem shoudnt even apply, and two, the reasoning is a bit fishy, just because the divergence diverges at zero, does this give a firm justification for assuming that the divergence is EQUAL to 4piδ

the reasoning in math is pretty sloppy

2)also another question, when deriving the vector potential it arrives at poisson's equation, my question is that does the pission's equation always have a solution(though it may not be in closed form) ? (that was needed to find a divergenceless vector potential for B)

thanks