# Thread: Potential Function of a Vector Field

1. ## Potential Function of a Vector Field

Alright so I have no idea what im doing and I cant seem to figure it out

from what I can tell a vector field is generally, although not always, just the gradient of the potential field

so I have this question to answer:
Find a potential for the vector field F by inspection.
F = <yz^2,xz^2,2xyz>

i thought it would simply be phi(x)=xyz^2
thought this is not that case
what am i doing wrong?

2. If I understand this you're looking for a function $\phi (x,y,z)$ such that $\nabla \phi(x,y,z)=F(x,y,z)$. If this is the case, simply derive and check that your answer is correct (It is, if this is what you meant anyway).

3. Originally Posted by TheUnfocusedOne
Alright so I have no idea what im doing and I cant seem to figure it out

from what I can tell a vector field is generally, although not always, just the gradient of the potential field

so I have this question to answer:
Find a potential for the vector field F by inspection.
F = <yz^2,xz^2,2xyz>

i thought it would simply be phi(x)=xyz^2
thought this is not that case
what am i doing wrong?
I assume a scalar potential is required. In which case your answer is correct. Why do you think it's wrong? (Note: The question says "Find a ....", not "Find the ..." If it was "Find the ..." then you would have to add a constant to your answer).