Two identical particles, each having charge 1q, are fixed in space and separated by a distance d. A third particle with charge 2Q 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 those charges (Fig. P23.20). (a) Show that if x is small compared with d, the motion of 2Q is simple harmonic along the perpendicular bisector. (b) Determine the period of that motion. (c) How fast will the charge 2Q be moving when it is at the midpoint between the two fixed charges if initially it is released at a distance a ,, d from the midpoint?