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B Infinity as a reference.

  1. Dec 20, 2016 #1
    I'm facing a problem in my physics course which is accepting that infinity can be a reference point in both Electrostatics (calculating the voltage of a point) and Matter Properties (calculating the gravitational potential energy), how come we use a reference point which we don't know where it is, keep in mind that I don't have any problems dealing with infinity when we plug it in a mathematical relation, what I want is to understand the physical concept of choosing infinity as a reference.
     
  2. jcsd
  3. Dec 20, 2016 #2

    A.T.

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    There is no general physical concept. It's often just a convenient convention
     
  4. Dec 20, 2016 #3

    PeroK

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    "A point at infinity" is simply a point far enough away that going any further would make a negligible difference to the system. E.g. the point at infinity is far enough away that the potential energy is a maximum (for GPE or attractive charges) or a minimum (for repulsive charges).
     
  5. Dec 20, 2016 #4
    Ok then, I can't get over that "convenient convention", and please tell me, what makes it legit ?
     
  6. Dec 20, 2016 #5
    Thanks for your reply, but can you tell me how we are able to calculate for instance the voltage of a point charge having a charge Q, it's coordinates are (X,Y) while setting our reference point as infinity ?
     
  7. Dec 20, 2016 #6

    PeroK

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    Voltage is the difference in electric potential, so the question is how to define electric potential. One definition of electric potential for a point charge ##Q## is:

    ##U = \frac{Q}{4\pi \epsilon_0 r} \ ##, where ##r## is the distance from the charge.

    This gives a function of ##r## that tends to ##0## as ##r \rightarrow \infty##. And, in many ways, this is the most natural and useful definition, given the relationship between ##U## and ##r##. I'm not sure I would say this uses ##\infty## as a reference point, though.

    You could equally well define:

    ##U = U_0 + \frac{Q}{4\pi \epsilon_0 r} \ ##, where ##U_0## is some constant.

    If ##Q## is negative (or if ##Q## is positive and ##U_0## is negative), you will have some radius ##r_0## where ##U(r_0) = 0##. But, it's not really making ##r_0## special.
     
  8. Dec 20, 2016 #7

    PeroK

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    PS How you define ##U(r)## doesn't change the critical fact that the function ##U(r)## never attains its max or min, but tends to one of these as ##r \rightarrow 0## and the other as ##r \rightarrow \infty##. In a sense, ##r \rightarrow \infty## has a physical meaning whether you like it or not!
     
  9. Dec 20, 2016 #8

    A.T.

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    This might be the core of your confusion: We aren't using the position as reference, just the finite value at which some function converges.
     
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