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Electric field problem

  1. Jan 22, 2006 #1
    A charge of -4.84 [tex] \mu C [/tex] is located at the origin, and a charge of -6.22 [tex] \mu C [/tex] is located along the y-axis at 1.361 m. The value of the Coulomb constant is 8.99 x 10^9. At what point along the y-axis is the electric field zero. Answer in units of m.
    I know that for the electric field to be zero, the electric field on the charges must equal each other.
    I called the distance from the charge at the origin R, and the distance from the second point is d-r.
    I used the equation for electric field and set them equal to each other.
    [tex] kQ/r^2= kq/(d-r)^2 [/tex]
    [tex] Q/r^2 = q/ (d-r)^2 [/tex]
    [tex] Q(d-r)^2 =qr^2 [/tex]
    [tex] (d-r)^2 =qr^2/ Q [/tex]
    [tex] (d^2 -2dr + r^2)/ r^2 = q/Q [/tex]
    [tex] d^2/r^2 - 2d/r +1 = q/Q [/tex]
    At this point I got stuck on how to solve for r, can someone help me?
    Thanks in advance.
     
  2. jcsd
  3. Jan 22, 2006 #2

    Pyrrhus

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    Homework Helper

    Here's some help
    [tex] (d-r)^2 =qr^2/ Q [/tex]
    [tex] d-r = r \sqrt{\frac{q}{Q}} [/tex]
     
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