1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook