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If you find the scalar potential of a conservative vector field

  1. Jun 30, 2005 #1
    Should your answer include the constant of integration? I think it should but my book's answers don't, so I dunno.

    Example, <2xy^3, 3y^2x^2>

    answer is x^2y^3, but should I include the + C? (and yes I went through and made sure h(y) was in fact a constant
    Last edited: Jun 30, 2005
  2. jcsd
  3. Jun 30, 2005 #2


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    Technically, yes, you should include it.
    Of course, a boundary condition might fix it to a specific constant.
    From a (classical) physical point of view, it's the "difference in potential" that is physically relevant.
  4. Jun 30, 2005 #3

    Doc Al

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    I would say yes. But it's OK to leave it out as long as you know that adding an arbitrary constant to the potential will produce the same vector field.
  5. Jun 30, 2005 #4

    Tom Mattson

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    Did the question ask for "the" scalar potential? If so, then go to your teacher and toss a hot cup of coffee in his lap. Once you've got his attention, explain to him that scalar potentials for a given force field aren't unique.

    Or did the question ask for "a" scalar potential? If so, then any one will do.
  6. Jun 30, 2005 #5
    Haha, hey, I like my teacher! It's actually outta the book, and it does say >A< scalar potential, had I been thinking it would've been clear, thanks though!
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