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Point Where Electric Field=0 (3 point charges on x-axis)

  1. Jan 11, 2013 #1
    1. The problem statement, all variables and given/known data
    Point charges of -7 µC, 1.0 µC, and +7 µC are located along the x axis at x = -1.0 cm, x = 0, and x = +1.0 cm, respectively. Locate a point on the positive x axis where the magnitude of the electric field is zero.


    2. Relevant equations
    E=(kQ)/r^2
    E(total)=E(1)+E(2)+E(3)

    3. The attempt at a solution

    I feel like I have the correct setup of the equation and just wanted to confirm:

    E=0=-(7e-6/(x+1)^2)+(1e-6/(x^2))-(7e-6/(1-x)^2)

    From this point I'm not really sure on how to proceed with solving for x.
     
  2. jcsd
  3. Jan 11, 2013 #2
    You need to isolate the x, so you should multiply out the exponent and rearrange the problem in order to use the quadratic equation.

    Edit: Actually don't isolate the x, just multiply the exponents out and group the similar exponents out.

    Edit 2: Hmm, its not working for me, disregard post
     
    Last edited: Jan 11, 2013
  4. Jan 11, 2013 #3

    gneill

    User Avatar

    Staff: Mentor

    Tip: When you're looking for zeros, you can discard all the common constants (same as setting your equation to zero and dividing both sides by the common constants). So your equation then looks like:

    $$0 = \frac{-7}{(1 + x)^2} + \frac{1}{x^2} + \frac{-7}{(1 - x)^2}$$

    Putting that over a common denominator and taking just the numerator yields a function that doesn't look promising for having positive real roots.

    Edit: I take that back! I made a silly sign error on the last term (now fixed). There is a root betwixt 0 and 1.
     
    Last edited: Jan 11, 2013
  5. Jan 13, 2013 #4
    Aaaaah I see, Thank you!
     
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