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Forces from a cherged ring onb a charged particle

  1. Jan 25, 2009 #1
    1. The problem statement, all variables and given/known data
    A charge, Q, is equally distributed in a small wireformed as a circle with radius R. Another charge, q, is placed at a distance R above the midpoint of the circle.
    What force affects the charge q?

    2. Relevant equations
    [tex]F = \frac{Qq}{4 \pi \varepsilon_0 r^2}[/tex]

    3. The attempt at a solution
    A distance , a, between a segment of the ring, dl, and q is [tex]a=\sqrt{2}R[/tex]. We set the z-axis as the normal of the midpoint of the circle. We split the forces (if we think of Q as split into small segments, dQ) on q into forces along the z-axis and forces parallell to the xy-plane. The forces parallell to the xy-plane cancel each other out, and the forces along the z-axis add upp. Since [tex]a=\sqrt{2}R[/tex] the z-resultant of the force would have a factor [tex]2[/tex], the force on q add upp to [tex]F = \frac{Qq}{4 \pi \varepsilon_0 (R/\sqrt{2})^2}[/tex].

    However, the answer in my problem collection says the answer should be [tex]F = \frac{Qq}{4 \pi \varepsilon_0 \sqrt{2}(\sqrt{2}R)^2}[/tex]. Which answer is the right one?
    Last edited: Jan 25, 2009
  2. jcsd
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