1. Not finding help here? Sign up for a free 30min 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!

Where is the electric field is zero?

  1. May 18, 2004 #1
    two charges of 1.5X10^-6 c and 3.0X10^-6 c are 0.2 m apart. Where is the electric field between them equal to zero?

    heres what i got....

    the electric field will be 0 when the field strength of the first charge minus the field strength of the second charge equals 0.

    therefore,

    q(1)-----x------P-------(0.2 - x)-------q(2)

    where...
    P is where the electric field equals 0
    q(1) is the first charge
    q(2) is the second charge
    x is the distance (in metres) from the charge

    [ kq(1) / (x)^2 ] - [ kq(2)/ ((0.2-x)^2) ] = 0

    from here,
    i cancel out the k's
    find the common denominator and cancel it out once my numerator is expanded
    try and use the quadratic equation to solve for x. however, when i try to solve for x i get a complex number...what am i doing wrong? the book says the answer is 0.08m (approx.) if you know a faster and much easier way, please do tell...thanks a bunch...
     
  2. jcsd
  3. May 18, 2004 #2

    Janitor

    User Avatar
    Science Advisor

    Let the neutral point be a distance r from the smaller charge Q and a distance R-r from the bigger charge 2Q. Note that

    kQ/r^2 - 2kQ/(R-r)^2 = 0 expresses the neutrality of the electric force along the line between the charges, by Coulomb's law.

    After some algebraic manipulation you get

    r^2 + 2Rr - R^2 = 0.

    Applying the quadratic formula,

    r = -R +/- sqrt(2)R. (I am too lazy to figure out how to stack the plus or minus symbol, so I wrote it as +/-.)

    Discard the root that does not lie between the two charges. This leaves you with

    r = [sqrt(2) - 1]R.

    Here R=0.2 m, so you have

    r = [1.414 - 1] 0.2

    which works out to about 0.08 meters, that being the distance from the smaller charge.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Where is the electric field is zero?
Loading...