Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1997
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1997

[Date Index] [Thread Index] [Author Index]

Search the Archive

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

--
Birthdays are good for you:  A federal funded project has recently determined
that people with the most number of birthdays will live the longest.....
-=><=-+-+-=><=-+-+-=><=-+-+-=><=-+-+-=><=-+-+-=><=-+-+-=><=-+-+-=><=-+-+-=><=-
     I BOYCOTT ANY COMPANY THAT USES MASS ADVERTISING ON THE INTERNET



  • Prev by Date: Why does TimeUsed die?
  • Next by Date: Re: Re: Problems with TimeConstrained in Win3.1
  • Previous by thread: Re: wrong divergence?!?
  • Next by thread: Re: wrong divergence?!?