- #1
jacquelinem_00
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Homework Statement
A vector field is defined by F(x) = (y+z, x+y, x+z).
Find the Jacobian and determine if the field is conservative in a finite region. If it is conservative, find the potential function.
Homework Equations
F = delta p AKA
F = (upsidedown triangle) p
The Attempt at a Solution
I found the Jacobian and determined that the field is conservative in a finite region. My problem is finding the potential function. So far I got:
dp ---> x(y+z) + C(y,z)
dx
dp ---> 1/2y (2x + y) + C(x,z)
dx
dp ---> 1/2z (2x + z) + C(x,y)
dx
I'm not sure on finding the potential function. From examples I've seen Icn set C(x,z) and C(x,y) to both equal zero, and then make C(y,z) a constant (using only y and z) to make dp/dx equal the other ones. But do they have to be exactly equal to each other? I'm wondering if anyone would give me some help with finding this potential function, please. Any help is greatly appreciated! :!)