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Where electric field is zero

  1. Sep 1, 2011 #1
    1. The problem statement, all variables and given/known data

    Two particles with positive charges q_1 and q_2 are separated by a distance s.

    Along the line connecting the two charges, at what distance from the charge q_1 is the total electric field from the two charges zero?

    (Express your answer in terms of some or all of the variables s, q_1, q_2 and K =1/(4*pi*[itex]\epsilon[/itex]. If your answer is difficult to enter, consider simplifying it, as it can be made relatively simple with some work.)

    2. Relevant equations

    E = K*(q/(d)^2)
    E_net = E1 + E2

    3. The attempt at a solution

    Since both the charges are positive, my E_net = E1 - E2. So I can solve this by finding where E1 and E2 are equal.

    Setting the two equations equal I get K(q_1/s^2) = K(q_2/s^2)

    Since I'm just concerned with finding the distance from q_1 to the point where the e-field is zero, wouldn't my equation be:

    s_1 = (q_1 - (q_2/(s_2)^2)

    Since none of the variables are defined, I'm having a hard time figuring out how to choose my 's' (distance). Wouldn't the distance ('s') depend on the magnitude of the charge on q_1 and q_2? How can I show that algebraically without somehow renaming the distance variable something other than 's'?
     
    Last edited: Sep 1, 2011
  2. jcsd
  3. Sep 1, 2011 #2
    I'm not sure I understood you.
    s is a given distance between the two charges.
    You need to find a point between them in which the field is zero - in other words, like you wrote, that E1 = E2.
    Let's assume this point has the distance "x" from q1.
    What is then the distance of this point from q2? (draw it to yourself if you're having a hard time).

    Then use the appropriate formulas to deduce what x should be - in a similar manner to what you've done, but right this time :-)
     
  4. Sep 1, 2011 #3
    See I understand that the distance from q_2 would be equal to (total separation 's' - distance from q_2), I just don't know how to represent that with only being able to use the variable 's' representing the total separation.
     
  5. Sep 1, 2011 #4
    Nevermind, I figured it out.

    I didn't realize that if I put in another variable into the equation 'x = distance from q_1' that it would end up cancelling out during the simplification process.

    The answer for me would be:

    x = s/1 + sqrt(q_2/q_1)
     
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