- #1
Summer95
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Homework Statement
There is a collection of different force fields, for example:
$$F_{x}=ln z$$
$$F_{y}=-ze^{-y}$$
$$F_{z}=e^{-y}+\frac{x}{z}$$
We are supposed to indicate whether they are conservative and find the potential energy function.
Homework Equations
See Above
The Attempt at a Solution
Is it a conservative force if it is the gradient of a scalar field?
So if $$\vec{F}=(\frac{\delta u}{\delta x},\frac{\delta u}{\delta y},\frac{\delta u}{\delta z})$$
You also have to check that $$
\Delta\times\vec{F}=\vec{0}$$
Which is true.
So for this particular case the answer would be yes, it is conservative, because $$u(x,y,z) = ze^{-y}+xlnz$$ fulfills this requirement.
So the actual potential energy would just be $$-u(x,y,z)$$
Is this the whole process I can do for any three dimensional force field? Am I missing any subtle details here?
Thank you!