Practice question · True or false
Every vector field has the property that its line integral depends only on the endpoints.
Hints
- Which fields are path-independent?
- Try circulating around a loop.
Show the answer
False
Why
False. Only conservative fields are path-independent, equivalently, those with zero curl, or expressible as a gradient. A swirling field gives different answers along different paths and non-zero circulation round a closed loop. That is what separates a force storing potential energy from one that dissipates it.
Practise Line Integrals
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