Plotting electric field lines of a dipole

  1. I was given this equation as the lines of electric fields of a dipole(two opposite charges separated by a finite distance)
    e=(1/r^3)*((3cos^2(theta)-1)^2 +sin^2(2theta))^0.5
    and I was asked to plot it.
    I guess it must be something like this:
    but when I try to plot it in in polar coords.I dont get the output I expect.
    The question is is it the right equation?
  2. jcsd
  3. Hmm, I also graphed it with wolfram, and it appears to not follow the characteristics of a dipole. It more appears to follow the characteristics of the electric field for like charges, rather than unlike.
  4. I like Serena

    I like Serena 6,181
    Homework Helper

    Welcome to PF, silverfox! :smile:

    I checked what the equation is for an electric dipole and found this:

    If I work this out in polar coordinates, I get a slightly different formula than the one you have for what appears to be the magnitude of the electric field.
    (You can use that [itex]\mathbf{p} = qd\cos\theta \mathbf{\hat r} - qd\sin\theta \hat{\textbf{θ}}[/itex].)
    Can it be that you or someone else made a calculation mistake?
    Last edited: Dec 11, 2011
  5. I worked a bit more on the problem but I couldn't find an equation myself nor could plot the ones you said or I found on wikipedia...
    I was told that if E(r, theta) is the first equation I wrote then E(r, theta, t) would be the same thing times sin(wt) but I dont get it, How does time affect the electric field lines?
    And I also thought that p is a border between + and - charges in a dipole which is equal to qd and is a constant value am I wrong?
  6. I like Serena

    I like Serena 6,181
    Homework Helper

    In the link I gave you can find an equation for E containing only p and r as variables.
    If you substitute the p I gave in my post, you get E(r,θ).
    The formula you gave in the OP looks like |E(r,θ)|, but it is not quite right.

    It does not have a time dependency.
    To make it time dependent, you would need to make the 2 charges time dependent.

    p is the vector dipole moment, which is constant.
    It is given by p=qd, where -q and +q are the charges, and d is the constant vector from the negative charge to the positive charge.

    However, a constant vector is dependent on θ in polar coordinates, since the unit vectors change with θ.
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