Question

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. (#, #, #)

Answer 1

there isn't an easy way to do it

Answer 2

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.

Answer 3

can I show you the actual question and get your opinion on what to do from there?

Answer 4

yeah, that'd be helpful, cause in general there's not really a set method of doing it that I'm aware of

Answer 5

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.

Answer 6

as far as i know the identity is shown as :
(del)∗(FXG)=((del)crossF)dotG)−Fdot((del)crossG)

Answer 7

ah, okay, this is a bit of a trick, the divergence of a curl is always zero.

Answer 8

Ha! problem solved

Answer 9

oh wait, nvm, that wasnt in the question...

Answer 10

well the second part it kind of is no?

Answer 11

no, its the dot product with a curl, its different.

Answer 12

hmm..

Answer 13

so you are saying that F(dot)[del(cross)G)
is not.. a divergence of a curl?

Answer 14

I guess, yeah that wouldn't make much sense, because then why would they have that identity in the first place

Answer 15

.. if it was just zero

Answer 16

yeah, g(0) is all constants though, shouldnt the curl of it be zero?

Answer 17

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

Answer 18

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

Answer 19

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!

Answer 20

k, best of luck