You are working for a manufacturing company. Your supervisor has an idea for controlling the position of a small bead by using electric fields. The physical setup is shown in the figure below. Fixed beads Movable a bead fr +ng x -pq a -mq -mq Three fixed beads are secured along the y-axis, with a bead of charge +ng at the origin and charges of -mq a distance a above and below the origin. The values of m and n can be set by an operator. On an insulating wire laid along the x-axis, a movable bead with charge -pq is placed. By adjusting m and n, the movable bead can be moved to different equilibrium positions x along the wire. Your supervisor asks you to set up the system and test it. In particular, he asks for answers to the following questions. (a) If n = 6 in a particular test, what is the value of m that will place the movable bead in equilibrium at x = a? m = 8.46 (b) In a second test with n = 6, what is the value of m that will place the movable bead in equilibrium at x = 2a? m = 4.194 (c) If n = 6 and the largest you can make m is m = 13, what is the closest equilibrium position of the bead to the origin? (Give your answer in terms of a.) 0. X Apply the particle in equilibrium model to the movable bead, considering the forces on the bead due to the charged beads on the y-axis. a m n (d) You decide to impress your supervisor by finding the range of values of m/n that will place the bead in equilibrium somewhere along the x-axis. Note that m, n, and p are not necessarily integers. (Give your answer as an inequality. Use the following as necessary: m, n, p.) > 0.5