Halliday, Resnick & Walker — Coulomb's Law: Problem 36

36 Figure 21-25a shows an arrangement of three charged particles separated by distance \( d \). Particles \( A \) and \( C \) are fixed on the \( x \) axis, but particle \( B \) can be moved along a circle centered on particle \( A \). During the movement, a radial line between \( A \) and \( B \) makes an angle \( \theta \) relative to the positive direction of the \( x \) axis (Fig. 21-25b). The curves in Fig. 21-25c give, for two situations, the magnitude \( F_{net} \) of the net electrostatic force on particle \( A \) due to the other particles. That net force is given as a function of angle \( \theta \) and as a multiple of a basic amount \( F_0 \). For example on curve 1, at \( \theta = 180^{\circ} \), we see that \( F_{net} = 2F_0 \). (a) For the situation corresponding to curve 1, what is the ratio of the charge of particle \( C \) to that of particle \( B \) (including sign)? (b) For the situation corresponding to curve 2, what is that ratio?