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Problem with the Divergence Theorem

  1. Apr 30, 2004 #1
    I was wondering if someone could give me a hand here with 2b) on the following link.
    http://www.am.qub.ac.uk/users/j.mccann/teaching/ama102/2003/assignments/assign_8.pdf
    For part a) I got it to be equal to 3x^2+3y^2+3z^2+2y-2xy, and I'm hoping that's right!

    However, for part b) I can't seem to get the answer they're after at all. We haven't covered any examples of this in our lectures yet and we won't have any lectures before the homework has to be handed in due to May Day, so any help would be much appreciated. Just to make sure I started it off right, could you just check if this is correct or not (sorry, I'm no good with LaTex!)-

    triple integral of (3r^2sin^2(theta)cos^2(f)+ 3r^2sin^3(theta)sin^2(f) + 3r^2cos^2(theta) + 2rsin(theta)sin(f) - 2r^2sin^2(theta)cos(f)sin)f))r^2sin(theta)drdfdtheta

    where the integral with respect to r is within the limits 0 and a, with respect to f is 0 to 2pi and with respect to theta is 0 to pi (where f is the asimuthal angle or whatever it's called). I'd really appreciate if you could just ehck I've done that bit okay, because it'd be a bit pointless me running through it if the mistake was in the first line.

    Btw, the answer I get at the end has an 8 on the numerator instead of a 12, so the answer isn't completely far out so I'm hoping it's just a wee mistake somewhere. Thanks! :smile:


    Btw, sorry if this is posted in the wrong forum!
     
  2. jcsd
  3. Apr 30, 2004 #2

    arildno

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    The divergence should be 3r^(2). I'll look a bit further into this..
     
  4. Apr 30, 2004 #3

    arildno

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    Ok:
    If you go back to your vector field, you'll see that from both the j'th and k'th component, you will gain a 2xy term, but with opposite signs.
    In your original expression, you've ended up with 2y-2xy instead
     
  5. Apr 30, 2004 #4
    Ah so shold it look like this then-

    3x^2 + 3y^2 + 3z^2 ?

    Gah I can be so stupid with even the simplest things!

    Thanks for helping btw! :smile:
     
  6. Apr 30, 2004 #5

    arildno

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    That's what I got, too (3r^(2)).
     
  7. May 2, 2004 #6
    Btw, for part 3a), that's a mistake, right? I mean I keep getting xi - yj + (-y^2 - x)k and I asked one of the phd students about it and they got the same but I just want to check before I email the lecturer about it.......
     
  8. May 2, 2004 #7

    arildno

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    Agreed, he'll be writhing in shame..
     
  9. May 2, 2004 #8
    Hope that wasn't sarcasm there. :tongue:
     
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