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MathGroup Archive 1997

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Re: Divergence and Dirac Delta Function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg9142] Re: [mg9127] Divergence and Dirac Delta Function
  • From: Axel Schwalm <a3023575 at smail3.rrz.Uni-Koeln.DE>
  • Date: Tue, 14 Oct 1997 10:01:56 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

>I am a physics student currently enrolled in an upper level
>Electrodynamics course and, while playing around with Mathematica 3.0
>for Students, I discovered that if I tell Mathematica to compute the
>divergence of:      unit vector(r) / r^2 it will return the value of
>zero.  However, I know that, at the very least in Electrodynamics, the
>correct value should be:  4*Pi*(DiracDelta Function).  Is it possible to
>get Mathematica to output this value without explictly telling the
>program that this is the value?
>                                        Elvis Dieguez

******************************************
Dear Elvis,
whether You get "1" or "4*Pi" as a result from considering vector 
matters, depends on the unit-system You make use of (SI- or Gaussian 
system, physically speaking).
One simplifies calculations, the other one is easier to understand (and 
to make a lecture with it).
Thus, Mathematicas result is as correct as Yours. In the long run, You 
will get used to switch between both description and discover, that 
"4*Pi" is an integrational constant, that comes all along in 
electrodynamics.
To understand the different descriptions, look, for example, into the 
courses of Feynman and Landau-Lifschitz.

Yours,
Axel Schwalm
University of Cologne


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