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Homework Help: Finding the accuracy of an approximated potential

  1. Feb 4, 2015 #1
    1. The problem statement, all variables and given/known data
    Charges +/- q separated by a distance d make a dipole with dipole moment qd. For large r the potential approaches qdcosθ/(4πε0r²). For θ=0, how large must r be so that the asymptotic function is accurate to 1%?

    2. Relevant equations
    Exact V= q1/(4πε0r) + q2 /(4πε0r)
    Approximate V= qdcosθ/(4πε0r²)

    3. The attempt at a solution
    I understand that the following statement must be true:
    Vexact - Vapproximate ≤ 1.0%(Vexact)

    q1/(4πε0r) + q2 /(4πε0(r-d)) - qdcosθ/(4πε0r²) ≤ 1.0 %.

    If we cancel all like constants;
    1/r - 1/(r-d) - d/r²) ≤ 1.0 %

    I do not understand where to go from here, or even if my approach towards this is correct.

    Thank you in advance to all those who are reading.
  2. jcsd
  3. Feb 4, 2015 #2
    I think they meant for you to have the two charges at +d/2 and -d/2. When you get the two fractions, you should reduce them to a common denominator. Then, you might get an idea what to do next.

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