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qwerty54321

Is it true that if F is a plane vector field such that ∮_c(F.dr)=0 for every closed curve C, then ∫_c(F.dr)=0 for every curve C? Please explain.

  • one year ago
  • one year ago

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  1. stephalia
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    ya

    • one year ago
  2. qwerty54321
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    Could you explain why please?

    • one year ago
  3. klimenkov
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    Something tells me that it is not right.

    • one year ago
  4. Spacelimbus
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    can you please check your opening post again @qwerty54321, is it all right written out? If F is a potential function then the gradient of that function with dr in a closed path will result to 0, that is true. But I have troubles understanding the post above.

    • one year ago
  5. qwerty54321
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    sorry here is the problem with proper notations

    • one year ago
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  6. Spacelimbus
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    I would agree with that yes, for every closed curve C. Path Independance.

    • one year ago
  7. qwerty54321
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    if it is not a closed curve, would the second part still hold true?

    • one year ago
  8. Spacelimbus
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    No in this case it's path independent, but it's integral depends on the value of the end points.

    • one year ago
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