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Uniform Field

  1. Aug 29, 2009 #1
    Moderation Note: Split from the original thread, which can be found https://www.physicsforums.com/showthread.php?p=680746#post680746"

    A uniform field does not have potential difference:smile:
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Aug 29, 2009 #2

    Doc Al

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    Re: Gravity inside the Earth

    Really?
     
  4. Aug 29, 2009 #3
    Re: Gravity inside the Earth

    It doesn't. Since the force everywhere is the same
     
  5. Aug 29, 2009 #4

    Vanadium 50

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    Re: Gravity inside the Earth

    And force is the rate of change of potential.
     
  6. Aug 29, 2009 #5
    Re: Gravity inside the Earth

    Right
     
  7. Aug 29, 2009 #6
    Re: Gravity inside the Earth

    No Since the work done in bringing a unit mass from infinity to any point would be infinite, there is no potential difference
     
  8. Aug 29, 2009 #7
    Re: Gravity inside the Earth

    Intuition works
     
  9. Aug 29, 2009 #8

    Vanadium 50

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    Re: Gravity inside the Earth

    If the force is constant (and non-zero) and the potential is the rate of change of force, the potential cannot be constant.

    That's simply not true.


    I wouldn't trust it. It's leading you astray.
     
  10. Aug 29, 2009 #9
    Re: Gravity inside the Earth

    The rate of change of potential is force:smile:
    But not here


    [qoute]
    That's simply not true.[/quote]Why not true?The definition of potntial is the work done to bring a unit mass from infinity to a point, and is infinite here since the force is constant all over.In the classical case, force at infinity is zero
     
  11. Aug 29, 2009 #10
    Re: Gravity inside the Earth

    Ah, you're too busy. I can see three in a line
     
  12. Aug 29, 2009 #11

    Doc Al

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    Re: Gravity inside the Earth

    The potential difference between any two points will be the work done to move a unit mass between those two points. (In some cases it makes sense to define the potential at infinity equal to zero, but not if the field is everywhere uniform.) Clearly the potential varies along the line of the force.
     
  13. Aug 30, 2009 #12
    Re: Gravity inside the Earth

    True, but here the potential at every point in the field is infinite, so there's no difference
     
    Last edited: Aug 30, 2009
  14. Aug 30, 2009 #13

    Vanadium 50

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    Re: Gravity inside the Earth

    This is just plain wrong. You can't define the potential at one point to be infinity, then calculate that at another point it's also infinity, so the difference between them is zero. Apart from not being the way to solve the problem, this is mathematically incorrect.

    A constant field has a potential growing linearly with distance.
     
  15. Aug 30, 2009 #14
    Re: Gravity inside the Earth

    It is mathematically incorrect, the answer is actually uncertain.
    I made use of the fact that since everywhere in the field the force on a unit mass is the same, the potential everywhere is the same too, but this does not go well with the math
    There is no imbalance in this field, and hence there should be no potential difference.
    But this is not real, and hence the answer is not real
     
    Last edited: Aug 30, 2009
  16. Aug 30, 2009 #15

    Doc Al

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    Re: Gravity inside the Earth

    That "fact" is just plain wrong. Since the force = -dU/dx, the potential cannot be the same everywhere.
     
  17. Aug 30, 2009 #16

    Hootenanny

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    Re: Gravity inside the Earth

    I haven't read this thread in it's entirety, but I would like to comment on your last post:
    As you say, this does not "go with the math" and is therefore incorrect! If there force on a unit mass is the same everywhere, that doesn't mean that potential is the same! In one dimension, the force is defined thus,

    [tex]F = -\frac{dV}{dx}[/tex]

    We assume that the force is constant,

    [tex]\frac{dV}{dx} = \text{const}[/tex]

    The potential is then (denoting the constant c1),

    [tex]V = c_1x + c_2[/tex]

    Hence, the potential is not the same everywhere!

    EDIT: Doc Al beat me to it :frown:
     
  18. Aug 30, 2009 #17
    Re: Gravity inside the Earth

    Vanadium said that a lot earlier. And I replied "the potential at a point is the work done to bring a unit mass from infinity to that point and thus the potential everywhere in this field
    is infinite"
    Read my edited previous post.
    There is no real answer to this because the situation itself is not real
     
  19. Aug 30, 2009 #18

    Hootenanny

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    Re: Gravity inside the Earth

    vin300 do you or do you not agree that the definition of force is the negative gradient of the potential? Please answer this question directly.
     
  20. Aug 30, 2009 #19

    DrGreg

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    Re: Gravity inside the Earth

    Exactly the problem. There is no such place as "at infinity", so trying to calculate the potential "at infinity" is where your logic goes wrong. You can't treat infinity like a real number and try to do maths with it. Think about what's really happening, without bringing infinity into it, and you should be able to make sense of it.

    When we say "it takes an infinite amount of work to move to infinity" you can't take that literally. It's a shorthand for saying, "the further you go, the more work is required, without any upper limit".

    Don't forget that you can always add a constant to a potential, you don't have to evaluate it "at infinity" to decide what it is elsewhere.
     
  21. Aug 30, 2009 #20
    Re: Gravity inside the Earth

    If you have read all my posts,:
    Yes, I agree the force is the negative gradient of potential, this is a fact
    Here there is a fixed force with an uncertain difference of potential, which is what makes the thing unreal
     
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