Practice question · Multiple choice
A line integral in a conservative field depends only on the endpoints. What does that imply about a closed loop?
Hints
- Set the endpoint equal to the start point.
- What would a nonzero loop integral let you build?
Show the answer
C. That the integral around any closed loop is zero
Why
Same endpoints, zero difference. A nonzero loop integral would let you gain energy by going round in a circle, which is why "conservative" and "has a potential" are the same statement.
Practise Line Integrals
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More questions on Line Integrals
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