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MathGroup Archive 1997

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Re: Divergence and Dirac Delta Function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg9154] Re: [mg9142] Divergence and Dirac Delta Function
  • From: Peter Jay Salzman <psalzman at landau.ucdavis.edu>
  • Date: Thu, 16 Oct 1997 03:37:55 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

> >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

> 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).


is this correct?  i was under the impression that the 4 pi came from
doing the surface integral around a sphere centred at the origin.  the
radial dependence drops out (1/r^2 cancels with the r^2 in the
differential area element) and you're left with 4 pi.

i think this result is invariant under change of unit system.

or am i remembering incorrectly?

peter

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