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At what point is the system in equilibrium?

  1. Oct 26, 2015 #1
    1. The problem statement, all variables and given/known data
    This is more of a math question but:

    There are two particles fixed in place: a particle of charge +8q at the origin and a particle of charge -2q
    at x=L. At what point (other than infinitely far away) can a proton be placed so that it is in equilibrium

    2. Relevant equations


    3. The attempt at a solution
    The point should be at the right of the -2q charge, so it is farther away from the charge +8q.

    upload_2015-10-26_7-33-56.png

    upload_2015-10-26_7-34-40.png

    upload_2015-10-26_7-35-2.png

    diagram:
    upload_2015-10-26_7-35-33.png

    that was the answer, but would it be possible to use

    8q / (L+x)2 = 2q / (x)2

    where L is the distance between the charges 8q and -2q.

    I get x = L using this set up instead.

    what went wrong? Shouldn't I get the same answer?
     
  2. jcsd
  3. Oct 26, 2015 #2

    Doc Al

    User Avatar

    Staff: Mentor

    The answers are the same! Realize that in the second approach you are measuring x from the second charge, not the origin.
     
  4. Oct 26, 2015 #3
    Ah, so the point is L away from the -2q and 2L away from the origin.
     
  5. Oct 26, 2015 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Exactly. What's confusing you is that in the second method, "x" stands for "unknown", not the x-coordinate of the final location. You'll have to translate to that to report your answer, if you want them to match.
     
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