All Questions
6
questions
1
vote
3
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106
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The conservative force [closed]
I read about the definition of the curl.
It's the measure of the rotation of the vector field around a specific point
I understand this, but I would like to know what does the "curl of the ...
- 11
2
votes
1
answer
200
views
What is the vector field associated with potential energy?
The mere concept of a line integral is defined for a vector field, and I thus thought the following was a rigorous and general definition of potential energy:
Definition: Given a conservative force ...
- 379
-1
votes
1
answer
37
views
Conservation and potential with non-cartesian forces
I understand how to determine if a force is conservative from
\begin{equation}
\nabla\times \mathbf{F}=0 \implies \mathbf{F}\text{ is conservative}
\end{equation}
When $F$ is in cartesian coordinates.
...
- 19
0
votes
2
answers
201
views
Potential Minimum Confusion
Today my lecturer mentioned the notion of vector field and potential, he also said that if the vector field is a force field then there is a potential energy given by: $F(x)=-\dfrac{dU}{dx}$. (I have ...
- 157
1
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0
answers
20
views
Are the gradient field are the only fields which are only conservative? [duplicate]
I have found that gradient fields are always conservative. But for my knowledge I wanna ask "are the gradient fields are only fields which are conservative"? I mean is it necessary that a field which ...
- 1,149
1
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2
answers
2k
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Does path independence of line integral imply that the given vector field is conservative (that is, it is negative gradient of some scalar potential)?
For a vector field, is path independence of line integral a necessary and sufficient condition for the field to be conservative or is it just a necessary condition? Please provide proof if possible.
- 121