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: Limit at infinity of an electric quadrupole

  1. Sep 7, 2008 #1
    This is for my intro physics 2 class
    1. The problem statement, all variables and given/known data
    Consider the charges Q at (-a, 0), -2Q at (0, 0) and Q at (a, 0). Such a combination of charges, with zero net charge and with zero net dipole moment, is called an electric quadrupole. a. Find the electric field along the x acis, for x > a. b. Show that, for x >> a, the electric field varies by x^-4. Find the coefficient.

    2. Relevant equations
    [tex]\vec{E} = \frac{kQ}_{r^{2}}\hat{r}[/tex]

    Here is the answer I got for part a which was correct.

    [tex] \vec{E} = kQ\left[\frac{1}_{(x+a)^{2}}} + \frac{1}_{(x-a)^{2}}} - \frac{2}_{x^{2}}}\right]\hat{j}[/tex]

    3. The attempt at a solution

    This is what I got for part b:

    [tex] \vec{E} = 2kQ\left[\frac{1}_{x^{2}}} - \frac{1}_{x^{2}}}\right]\hat{j} = 0[/tex]

    I don't know how to get the book's answer of

    [tex] \frac{6a^{2}}_{x^{4}}}\hat{j} [/tex]
  2. jcsd
  3. Sep 7, 2008 #2


    User Avatar
    Homework Helper

    Hi Monocles,

    You do not want to set:

    \frac{1}{(x+a)^2} \longrightarrow \frac{1}{x^2}
    because you'll lose the part you're looking for.

    Have you seen the binomial series approximation formula for [itex](1+y)^p[/itex] when y is small? You can write your quantity [itex]\frac{1}{(x+a)^2}[/itex] (and the other term, too) in that form and then use the formula to get the answer.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook