Two identical particles, each having charge #q, are fixed in space and separated by a distance d. A third point charge -Q is free to move and lies initially at rest on the perpendicular bisector of the two fixed charges a distance x from the midpoint between the two fixed charges (Fig. P23.12)
(a) Show that if x is small compared with d, the motion of -Q will be simple harmonic along the perpendicular bisector. Determine the period of that motion.
(b) How fast will the charge -Q be moving when it is at the midpoint between the two fixed charges, if initially it is released at a distance a