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Columb distance/charge balancing problem

  1. Jan 25, 2009 #1
    1. The problem statement, all variables and given/known data
    A meter stick has two charges placed on it at the 0 mark is a charge of +1 coulomb. On the 100cm mark is a charge of +4 coulombs. Where should a proton be placed on the meter stick so that the net force due to both charges is 0.

    2. Relevant equations

    Kc = Coulomb const.
    Q= charge
    a=unknown distance from +1 on proton
    b= unknown distance from +4 on proton
    X= proton on line
    (Kc*Q1*Qn)/r^2= Force 1 on n

    3. The attempt at a solution

    So far I've attempted to do the following:
    The proton must fall in some region between the two.
    If we take 50cm to be the origin of this system and 100 to be +50cm and -50 to be the negative maximum the system at 0 then the +1 charge acts on it towards the negative X direction. So it goes from this:


    -[(Kc*Qproton*Q+1)/a^2]+(Kc*Qproton*Q+4)/b^2 = 0
    This however, gives me:

    Which to me says that in order for this equation to be true then the distance to the proton on the +4 charge must be twice that of the distance from +1. However I can't seem to find any reasonable way to put this on the meter stick. The only possibility I can think of that would follow this is that the proton must be 30cm from the +1 charge and 60cm from the +4 charge but this still leaves 10cm that don't exist on the meter stick.

    Have been working on this for a few hours now and am beginning to think maybe I'm thinking about this the wrong way. Any help is greatly appreciated.
  2. jcsd
  3. Jan 25, 2009 #2


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    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Specialmias! Welcome to PF! :smile:

    Yes, you're right … the distance to the proton on the +4 charge must be twice that of the distance from +1.

    Now calm down!

    just use algebra …

    start by saying "if the distance from the 0 cm mark is x cm, then … " :wink:
  4. Jan 25, 2009 #3
    Oh wow. 3X completely whooshed by my head. You've saved my sanity, thank you.
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