Halliday, Resnick & Walker — Electric Fields: Problem 53

53 Two charged beads are on the plastic ring in Fig. 22-45a. Bead 2, which is not shown, is fixed in place on the ring, which has radius $R = 40.0 \text{ cm}$. Bead 1, which is not fixed in place, is initially on the $x$ axis at angle $\theta = 0^\circ$. It is then moved to the opposite side, at angle $\theta = 180^\circ$, through the first and second quadrants of the $xy$ coordinate system. Figure 22-45b gives the $x$ component of the net electric field produced at the origin by the two beads as a function of $\theta$, and Fig. 22-45c gives the $y$ component of that net electric field. The vertical axis scales are set by $E_{xs} = 5.0 \times 10^4 \text{ N/C}$ and $E_{ys} = -9.0 \times 10^4 \text{ N/C}$. (a) At what angle $\theta$ is bead 2 located? What are the charges of (b) bead 1 and (c) bead 2?