Two positive point charges Q are held fixed on the x-axis at x = a and x = -a. A third positive point charge q, with mass m, is placed on the x-axis away from the origin at a coordinate x such that |x| «a. The charge q, which is free to move along the x-axis, is then released.
(a) Find the frequency of oscillation of the charge q. (Hint: Review the definition of simple harmonic motion in Section 13.2. Use the binomial expansion (1 + z) n = 1 +nz + n (n - 1)z2/2 +.. .., valid for the case |z| < 1.)
(b) Suppose instead that the charge q were placed on the y-axis at a coordinate y such that |y| «a, and then released. If this charge is free to move anywhere in the xy-plane, what will happen to it? Explain your answer.