Question

You are working for a manufacturing company. Your supervisor has an idea for controlling the position of a small bead by using electric flelds. The physical setup is shown In the figure below. 1 Fixed beads Tmg Movable bead tnq pg ng Three fixed beads are secured along the y-axis, with a bcad of charge +ng at the origin and charges of -ma 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 he 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 -5 in a particular test, what is the value of m that will place the movable bead in equilibrium atx - 87 (b) In a second test with n - 5, what is the value of m that will place the movable bead in equilibrium atx -287 (c) If n = 5 and the largest you can make m is m-11, what is the closest equilibrium position of the bead to the origin? (Give your answer in terms of a.) (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 ρ are not necessarily integers·(Give your answer as an inequality. Use the following as necessary: m,n, p)

Answer 1

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