Electric Field Due to Dipole Problem

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

    Consider the following figure.

    [​IMG]

    For the electric dipole shown in the figure, express the magnitude of the resulting electric field as a function of the perpendicular distance x from the center of the dipole axis. (Use the following as necessary: k, q for the charges, x, and d.)

    2. Relevant equations

    Et= E1 + E2

    E = k|q|/r2



    3. The attempt at a solution

    The x component of the electric fields will cancel out, leaving only the y-components. Adding the two vector fields in the y-direction:

    [k|q|/r2]sinθ + [k|q|/r2]sinθ = 2[k|q|/r2]sinθ

    r^2 = [d/2 + x^2]1/2

    My final answer:

    2[kq/[d2/4 + x2]1/2]sinθ

    This is not correct.
     
    Last edited: Feb 8, 2013
  2. jcsd
  3. Dick

    Dick 25,810
    Science Advisor
    Homework Helper

    For one thing r^2=x^2+(d/2)^2. You've got an extra square root. For another, you should be able to express sinθ in terms of x and d as well.
     
  4. Yes, I noticed that extra square root. When I fix things up, and set sinθ equal to d/2r:

    It's a lot of algebra, but it comes out to kqd/[(d2/4)+x2)]3/2. Does that look right?
     
  5. Dick

    Dick 25,810
    Science Advisor
    Homework Helper

    Looks ok to me.
     
  6. All right. Thanks. Webassign doesn't like the answer but I feel confident in the math. Could be a problem with Webassign.
     
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