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Coulomb's law point charges distance for 0 net force

  1. Jan 21, 2012 #1
    1. The problem statement, all variables and given/known data

    One charge of (+5µC) is placed in the air at exactly x = 0, and a second charge (+7µC) at x = 100cm. where can the third charge be placed so as to experience zero net force due to the other charges?

    2. Relevant equations
    F=KQ1Q2 / D^2

    3. The attempt at a solution
    Q1 = +5µC,
    Q2 = +7µC,
    Q3d from q1 = D1,
    K = 9*10^9,
    100 cm = 1 m
    1m - D1 = D2.

    Then the k's cancel each other out and the Q3's cancel each other out.


    Is this correct? also can you give me an example on solving this equation if it is correct?

    Another thing
    if Q1 had a smaller and opposite charge compared to Q2, the equation would be?
  2. jcsd
  3. Jan 21, 2012 #2
    Sorry i did not type out the values,


    saying that we are finding distance and both the charges are 10^-6 it can cancel out right?
    Sorry i guess this is more of a math problem if i have the formula right, i really am not sure how to solve this, i have tried but i keep getting the wrong answers. the answer in the book is .46m or 46cm
  4. Jan 21, 2012 #3


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    Homework Helper

    You meant D1 instead of d1, did you not? (q1)/(D1^2)=(q2)/(1-D1)^2 is correct. Cancel the factors 10^-6 . Take the reciprocal of both sides, expand the square, move everything to one side and solve the quadratic equation. You get two roots, exclude the one not between 0 and 1.

    Q1/D1^2=(q2)/(1+D1)^2 is the correct one.
    Last edited: Jan 21, 2012
  5. Jan 21, 2012 #4
    Thank you very much :P. I'm not 100% on solving quadratics however I have a 600 page math textbook that i'm working through right now that will cover it. My physics class is 1 year ahead of my math class. :S
  6. Jan 21, 2012 #5


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    Oh. Do not read all that 600 pages. If you have an equation of form ax2+bx+c=0 the solutions are

    [tex]x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] Can you manage?

  7. Jan 22, 2012 #6
    Thank you very much, i will play around with it however i am not to familiar with radicals so I'm not sure if i will be able to get through it :S
  8. Jan 22, 2012 #7


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    Oh. Your Physics class is very much ahead of your Maths class. The square root of a number x is the non-negative number denoted by √x which multiplied by itself gives out x.

    √x * √x = x.

    √4=2 , as 2*2=4
    √100=10 as 10*10 = 100.

    You certainly find a key on your calculator that corresponds to the square root operator.

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