# Forces from a cherged ring onb a charged particle

1. Jan 25, 2009

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
$$F = \frac{Qq}{4 \pi \varepsilon_0 r^2}$$

3. The attempt at a solution
A distance , a, between a segment of the ring, dl, and q is $$a=\sqrt{2}R$$. 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 $$a=\sqrt{2}R$$ the z-resultant of the force would have a factor $$2$$, the force on q add upp to $$F = \frac{Qq}{4 \pi \varepsilon_0 (R/\sqrt{2})^2}$$.

However, the answer in my problem collection says the answer should be $$F = \frac{Qq}{4 \pi \varepsilon_0 \sqrt{2}(\sqrt{2}R)^2}$$. Which answer is the right one?

Last edited: Jan 25, 2009