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Re: Re: wrong divergence?!?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg6401] Re: [mg6384] Re: wrong divergence?!?
*From*: peter <psalzman at landau.ucdavis.edu>
*Date*: Sun, 16 Mar 1997 19:25:15 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
> > when i take the divergence of:
> >
> > e = {q/r^2, 0, 0}
> >
> > i get zero. i remembered to load VectorAnalysis and SetCoordinates to
> > Spherical.
> Function Div returns a correct value. To check it calculate divergence in
> spherical coordinates to obtain:
>
> div (q/r^2, 0 , 0) = (1/r^2) * D[(r^2) * (q/r^2), r] = (1/r^2) * D[q,r] =
> 0.
> I assume that q does not depend on r.
yeah, q is a constant, but that's not the correct divergence when r=0.
in spherical coordinates we need to be careful at the origin, where there
are apparent singularities lurking.
i was wondering if MMA had the capability to see through them, but i
guess not from what someone had said via email.
the way to get the correct divergence at the origin is to calculate a
volume integral of div E in a sphere centred at the origin. use the div
theorem to convert to a surface integral. you'll see the answer is
independent of radius which means the contribution was solely at the
origin. however, we normally can't have an interval of zero measure
contributing to an integral, so there must have been a delta function at
the origin in the expression for div E.
peter
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