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qwerty54321

  • 3 years ago

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.

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  1. stephalia
    • 3 years ago
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    ya

  2. qwerty54321
    • 3 years ago
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    Could you explain why please?

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

  4. Spacelimbus
    • 3 years ago
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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.

  5. qwerty54321
    • 3 years ago
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    sorry here is the problem with proper notations

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

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

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

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