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Two charges and electric field?

  1. Jan 8, 2015 #1
    1. The problem statement, all variables and given/known data
    Two charged particles are located on the x axis. The first is a charge +Q at x= -a. The second is an unknown charge located at x= +3a. The net electric field these charges produce at the origin has a magnitude of 2kQ/a^2. Explain how many values are possible for the unknown charge and find the possible values.

    2. Relevant equations
    E=k(q/r^2)

    3. The attempt at a solution
    I got the right answer, I'm just not sure if my thinking is right, because I kind of ignored the way the electric is facing. First of all I assumed q is negative and got 2kQ/a^2=kQ/a^2-k1/9a^2 based on the attraction of q to Q. That turns out to be q=-9Q. Then I did the same thing for when q is positive and got 2Qk/a^2=qk/9a^2 - kQ/a^2, again based on the attraction of q and Q. That turns out to q=27Q, which are the right answer. Is this a valid way of doing it or am I thinking of it wrong?
     
  2. jcsd
  3. Jan 8, 2015 #2

    Bystander

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    Is there any particular doubt that stands out in your mind?
     
  4. Jan 8, 2015 #3
    My main doubt is that I'm not taking into account the way that the electric field is facing due to the two charges, or would that just be a different way of thinking of it? Only my 4th day of E&M so I'm not too great at it yet :/
     
  5. Jan 8, 2015 #4

    haruspex

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    Despite the way you worded your argument, trying both signs for the resultant field is precisely what you did.
    Correcting the typo in the first equation:
    2kQ/a^2=kQ/a^2-kq/9a^2​
    the only difference from the second equation is the sign of the whole right hand side - or, equivalently, of the left hand side.
     
  6. Jan 8, 2015 #5
    It's always the simplest parts that mess me up D:
    But thank you for the help, makes sense then!
     
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