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Homework Help: Where is the electric field zero

  1. Feb 20, 2015 #1
    1. The problem statement, all variables and given/known data
    A -10.0 nC point charge and a +20.0 nC point charge are 15.0 cm apart on the x-axis.

    a. What is the electric potential at the point on the x-axis where the electric field is zero?
    b. What is the magnitude of the electric field at the point on the x-axis, between the charges, where the electric potential is zero?

    2. Relevant equations
    E = kQ/r^2
    V = Ed
    U = kQq/r

    3. The attempt at a solution
    Let x be the distance from the -10nC point where the field is zero in cm
    r = .15m
    k = Coulomb's constant (8.99*10^9)
    q1 = -10nC
    q2 = 20nC
    I tried solving for where the electric field would be zero by first doing:
    [tex]0 = \frac{k*q_1}{(x)^2} + \frac{k*q_2}{(r-x)^2}[/tex]
    Solving for x, I got x = -0.36m and 0.062m

    I'm not really sure how to proceed from here since I have two points where it seems that the field is zero.
  2. jcsd
  3. Feb 20, 2015 #2
    You have a positive charge say at (a,0) and a negetive charge at (b,0). Obviously the electric field is non zero in between the charges. Your equation is incorrect because you assumed the required point to be in between a and b.(you took r to be the distance between the charges and x to be the distance from q1 to the required point, and the other is r-x).
    So change it to:
    $$0=\frac{kq_1}{x^2} + \frac{kq_2}{(r+x)^2}$$
    Same method is used for electric potential as well. Try to derive the expression for the point where the potential is zero. Then again find x.
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