divergence theorem- restrictions or conditions, field vector

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djoe

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divergence theorem

Hi everybody;
my question is:
why the field vector Ar=1/r² (sph. coord. syst.) doesn't verify the divergence theorem?
are there any restrictions or conditions on the field vector?
Thanks
 

Re: divergence theorem

Hello,

It actually does verify the divergence theoreme,
in spherical system, the divergence formula is :

div(A) = (1/r) * D(r² * Ar) / Dr + (1 / (r * sin(Θ)) * D(sin(Θ) * AΘ) / DΘ + (1 / (r * sin(Θ)) * D(AΦ) / DΦ.

For the field Ar = 1 / r², it will be 0 everywhere else than (0,0,0) !

slvn
 

Re: divergence theorem

I think learning about 3dimensional dirac delta function will help to understand the problem. Any good book of electro-statics will help.

It has the property ∫ div(r/r^3)dV = 4Π δ(r) where δ(r)has a value ∞ at r =O and O elsewhere. [/b]
 

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