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Find the unknown charges q1 and q2

  1. Jun 26, 2016 #1
    1. The problem statement, all variables and given/known data
    The geometrical positions of point-like charges and point A situated in the xy-plane in terms of the length parameter a. The vector of electric field E at point A is shown schematically and measured as E = Exi + Eyj (that is, both Ex and Ey are given). If possible, find the unknown charges q1 and q2.

    **E_2 is the electric field with respect to q2. Not shown in figure. **
    **E_1 is the electric field with respect to q1. (Same direction as E) **

    **k_e is Coulomb's constant.**

    Screen Shot 2016-06-26 at 2.40.14 PM.png

    2. Relevant equations
    E
    = Exi + Eyj
    Ex = E_1*cos(45°) - E_2*cos(45°)
    Ey = E_1*sin(45°) + E_2*sin(45°)
    E = F/q = (k_e*q)/r^2

    3. The attempt at a solution
    E_1
    = (k_e*q1)/(2a)^2 = (k_e*q1)/(4a^2)

    E_2 = (k_e*q2)/(2a)^2 = (k_e*q2)/(4a^2)

    Ex = (E_1 - E_2)*2/sqrt(2)

    Ey = (E_1 + E_2)*2/sqrt(2)

    E
    = 2/sqrt(2)*(E_1 - E_2) i + 2/sqrt(2)*(E_1 + E_2) j = 2/sqrt(2)*(k_e/(4a^2))*(q1 - q2) i + 2/sqrt(2)*(k_e/(4a^2))*(q1 + q2)


    I am stuck here; I'm not sure if I've been going about this correctly or what steps to take next.

    Thank you.
     
  2. jcsd
  3. Jun 26, 2016 #2

    SammyS

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    Hello JessieS , Welcome to PF !

    Are you given any numerical values, particularly any for Ex and Ey ?
     
  4. Jun 26, 2016 #3
    Thank you!

    And no I am not. I am supposed to just use Ex and Ey as variables.
     
  5. Jun 26, 2016 #4

    SammyS

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    OK.

    You are on the right track.

    First, at least one error. What is the distance from q1 to A and q2 to A. The square of each of those distances is 2a2, not 4a2 .

    I suggest that you keep Ex and Ey separate, rather than lumping them together into one big vector expression.

    You have that Ex = C⋅(q1 - q2) and Ey = C⋅(q1 + q2) , where the coefficient, C is made up of all that stuff in your equation.
     
  6. Jun 26, 2016 #5


    Ok, so could I do this?

    Since
    Ex = 2/√2*(q1 - q2)*(ke/(2a2))

    Ey = 2/√2*(q1 + q2)*(ke/(2a2))

    Then
    (q1 - q2) = (Ex * a2*√2)/ke
    + (q1 + q2) = (Ey * a2*√2)/ke
    --------------------------------
    q1 = (a2*√2)/ke * (Ex + Ey)

    So then

    q2 = (a2*√2)/ke * (Ey - Ex)

    Is that correct?
     
  7. Jun 26, 2016 #6

    SammyS

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    Yes. That's it.

    Subtracting should give q2.
     
  8. Jun 26, 2016 #7
    Thank you for your help! :smile:
     
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