Practice question · Select all that apply
Which conditions guarantee that a vector field F in ℝ² is conservative?
Hints
- Several of these conditions are equivalent restatements of each other.
- A condition about magnitude alone says nothing about rotation.
Show the answer
- A. ∮ F · for every closed curve
- C. = (where )
- D. for some scalar function
Why
Equal mixed partials, existence of a potential, and zero circulation are all equivalent.
Practise Line Integrals
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