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Homework Help: 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
    D1+D2=1m,
    1m - D1 = D2.

    K(q1*q3)/d1^2)=K(q2*q3)/(1-D1)^2
    Then the k's cancel each other out and the Q3's cancel each other out.

    (q1)/(d1^2)=(q2)/(1-D1)^2

    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?
    (q1)/(d1^2)=(q2)/(1+D1)^2
     
  2. jcsd
  3. Jan 21, 2012 #2
    Sorry i did not type out the values,

    5/d^2=7/(1+D)^2

    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

    ehild

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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

    ehild

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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?

    ehild
     
  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

    ehild

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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.



    ehild
     
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