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Homework Help: Electric Field at a Distant Point

  1. Jan 10, 2010 #1
    1. Consider the electric dipole on the x-axis where a positive charge q is at (a,0) and a negative charge -q is at (-a,0) such that the distance between the two charges is 2a. Show that the electric field at a distant point on the +x axis is
    E(x)= 4kqa/x^3.



    2. Relevant equations: E=kq1q2/r^2



    3. The attempt at a solution:

    E=kq/x^2 - kq/(x+2a)^2

    E(simplified)=kq[x^-2 - (x^2+4a)^-1]

    E=4kqa/(x^4+4x^2a)

    This clearly gives me the wrong solution, but I know it works when I switch my r values.

    Why is it that I have to use x-a and x+a for r instead of x and x-2a?

    Why does shifting the y-axis change the answer since x>>2a, it shouldn't matter, but I'm getting a different solution using this approach.

    Please help me understand this problem! Thanks!
     
  2. jcsd
  3. Jan 10, 2010 #2

    rl.bhat

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    E(simplified)=kq[x^-2 - (x^2+4a)^-1]

    E=4kqa/(x^4+4x^2a)

    Check this simplification.
    E = kq[1/x^2 - 1/(x + 2a)^2]
    = kq[(x+2a)^2 - x^2]/(x)^2*(x+2a)^2
    = kq[4ax+4a^2]/(x)^2*(x+2a)^2
    = kq*4ax*(1+a/x)/(x)^4(1+2a/x)^2
    Neglect a/x term and find E.
     
  4. Jan 11, 2010 #3

    vela

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    The second line is obviously wrong because you can't add [itex]x^2[/itex] to [itex]4a[/itex]. They have different units. It's not clear to me what you were trying to do.
     
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