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MathGroup Archive 1997

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Re: wrong divergence?!?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg6378] [mg6378] Re: [mg6346] wrong divergence?!?
  • From: seanross at worldnet.att.net
  • Date: Fri, 14 Mar 1997 14:54:30 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

peter wrote:
> 
> hi all
> 
> when i take the divergence of:
> 
>   e = {q/r^2, 0, 0}
> 
> i get zero.  i remembered to load VectorAnalysis and SetCoordinates to
> Spherical.
> 
> this is the electric field due to a point charge at the origin.  even
> though MMA doesn't know maxwell's equations, if we strip all the physical
> meaning from this vector field, shouldn't the divergence be something other
> than zero at the origin?
> 
> thanks!
> 
> peter



I don't have my copy of Classical Electrodynamics in front of me, but as 
I recall, the divergence of 1/r^2 is something like 4 Pi diracdelta(r) 
which means that it is identically zero everywhere but the origin.  As I 
recall from doing that derivation once, it is a little tricky and I 
wouldn't expect a program to catch on to something that subtle.  Once 
again, as wonderful as Mathematica is, there is no substitute for pencil 
and paper.


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