Practice question · Multiple choice
You must compute the work along a complicated spiral path, and you notice for some potential . What is the fastest correct move?
Hints
- The fundamental theorem for line integrals: for gradient fields, only the endpoints matter.
- Zero work is guaranteed only for closed loops. This path has distinct endpoints.
Show the answer
C. Evaluate at the endpoints: work
Why
Conservative fields make the path irrelevant: exactly, spiral or not. This is why potential energy exists, and why "work done against gravity" depends on height gained, never on the route taken.
Practise Line Integrals
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More questions on Line Integrals
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