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Electrical and gravitational forces of protons

  1. Jan 30, 2013 #1
    1. The problem statement, all variables and given/known data
    At what distance between two protons are the electrical and gravitational forces equal?


    2. Relevant equations
    electromagnetic Force = k(Q1*Q2/r^2)
    gravitational Force = G(m1*m2/r^2)

    Constants:
    k = 9.0*10^9 (N m^2/c^2)
    G = 6.673 × 10^-11 (m^3 kg^-1 s^-2)
    Charge of proton: 1.6*10^-19 C
    Mass of proton: 1.67*10^-27 kg

    3. The attempt at a solution
    I solved the first equation for r^2. Then, I substituted the second equation in for force since electromagnetic and gravitational force are equal in this problem. This seems logical, no? The only problem is, when I solve for r, the r's cancel out... :_(
     
    Last edited: Jan 30, 2013
  2. jcsd
  3. Jan 30, 2013 #2

    tms

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    At what value of [itex]r[/itex] does [itex]kq^2 = Gm^2[/itex]?
     
  4. Jan 30, 2013 #3
    When r approaches zero or when they are very close to one another, the gravitational force is as large as the electrical force. Both the forces approach infinity.
    or
    When r approaches infinity or when they are very far apart, the gravitational force and the electrical force approach zero.
    Make sense? I'm not so sure.
     
  5. Jan 30, 2013 #4

    tms

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    But they don't approach zero or infinity at the same rate.
     
  6. Jan 31, 2013 #5
    I believe that the question is: At what value of [itex]r[/itex] does [itex](kq^2)/r^2 = Gm^2/(r^2)[/itex]?
     
    Last edited: Jan 31, 2013
  7. Jan 31, 2013 #6
    They're never equal.

    That's why.
     
  8. Jan 31, 2013 #7
    Okay, thanks!
     
  9. Jan 31, 2013 #8

    tms

    User Avatar

    But, as you pointed out, the [itex]r[/itex]s cancel.
     
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