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anonymous

  • 4 years ago

Come on Calculus Friends!! If you are given curl i.e. (del (cross) F) what is the method to figure out what F is, when (del (cross) F) is a vector quantity i.e. (#, #, #)

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  1. anonymous
    • 4 years ago
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    there isn't an easy way to do it

  2. anonymous
    • 4 years ago
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    you've got yourself a lovely set of 3 partial differential equations. \[\frac{\delta u_y}{\delta z}-\frac{\delta u_z}{\delta y}=f(x,y,z) \hat{x}\] etc.

  3. anonymous
    • 4 years ago
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    can I show you the actual question and get your opinion on what to do from there?

  4. anonymous
    • 4 years ago
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    yeah, that'd be helpful, cause in general there's not really a set method of doing it that I'm aware of

  5. anonymous
    • 4 years ago
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    Let F and G be vector fields such that (del) X F(0) = (-6.914, 5.159, 4.502), G(0) = (-8.196, -1.838, -2.2). Find the divergence of F X G at 0.

  6. anonymous
    • 4 years ago
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    as far as i know the identity is shown as : (del)∗(FXG)=((del)crossF)dotG)−Fdot((del)crossG)

  7. anonymous
    • 4 years ago
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    ah, okay, this is a bit of a trick, the divergence of a curl is always zero.

  8. anonymous
    • 4 years ago
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    Ha! problem solved

  9. anonymous
    • 4 years ago
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    oh wait, nvm, that wasnt in the question...

  10. anonymous
    • 4 years ago
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    well the second part it kind of is no?

  11. anonymous
    • 4 years ago
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    no, its the dot product with a curl, its different.

  12. anonymous
    • 4 years ago
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    hmm..

  13. anonymous
    • 4 years ago
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    so you are saying that F(dot)[del(cross)G) is not.. a divergence of a curl?

  14. anonymous
    • 4 years ago
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    I guess, yeah that wouldn't make much sense, because then why would they have that identity in the first place

  15. anonymous
    • 4 years ago
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    .. if it was just zero

  16. anonymous
    • 4 years ago
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    yeah, g(0) is all constants though, shouldnt the curl of it be zero?

  17. anonymous
    • 4 years ago
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    so all you'll have is the dot product of the two? I could be wrong, but from what I see you're definitly not given enough information to reverse engineer the field for f out of what you have

  18. anonymous
    • 4 years ago
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    See, those are the types of things i'm still trying to grasp.. aha. it would be nice make things much easier

  19. anonymous
    • 4 years ago
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    okay then that must be the best bet, I have possible answers, so i'll try and if I get it I'll let you know either way. thank you for your help!

  20. anonymous
    • 4 years ago
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    k, best of luck

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