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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 mg a Movable bead +ng - pg a - mg Three fixed beads are secured along the y-axis, with a bead of charge +ng at the origin and charges of -mg 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 -pg 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 = 7 in a particular test, what is the value of m that will place the movable bead in equilibrium at x = a? m = (b) In a second test with n = 7, what is the value of m that will place the movable bead in equilibrium at x = 2a? m = (c) If n = 7 and the largest you can make m is m = 15, what is the closest equilibrium position of the bead to the origin? (Give your answer in terms of a.) 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 p are not necessarily integers. (Give your answer as an inequality. Use the following as necessary: m, n, p.)

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 mg a Movable bead +ng - pg a - mg Three fixed beads are secured along the y-axis, with a bead of charge +ng at the origin and charges of -mg 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 -pg 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 = 7 in a particular test, what is the value of m that will place the movable bead in equilibrium at x = a? m = (b) In a second test with n = 7, what is the value of m that will place the movable bead in equilibrium at x = 2a? m = (c) If n = 7 and the largest you can make m is m = 15, what is the closest equilibrium position of the bead to the origin? (Give your answer in terms of a.) 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 p are not necessarily integers. (Give your answer as an inequality. Use the following as necessary: m, n, p.)

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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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 mg a Movable bead +ng - pg a - mg Three fixed beads are secured along the y-axis, with a bead of charge +ng at the origin and charges of -mg 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 -pg 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 = 7 in a particular test, what is the value of m that will place the movable bead in equilibrium at x = a? m = (b) In a second test with n = 7, what is the value of m that will place the movable bead in equilibrium at x = 2a? m = (c) If n = 7 and the largest you can make m is m = 15, what is the closest equilibrium position of the bead to the origin? (Give your answer in terms of a.) 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 p are not necessarily integers. (Give your answer as an inequality. Use the following as necessary: m, n, p.)
Transcribed Image Text: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 mg a Movable bead +ng - pg a - mg Three fixed beads are secured along the y-axis, with a bead of charge +ng at the origin and charges of -mg 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 -pg 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 = 7 in a particular test, what is the value of m that will place the movable bead in equilibrium at x = a? m = (b) In a second test with n = 7, what is the value of m that will place the movable bead in equilibrium at x = 2a? m = (c) If n = 7 and the largest you can make m is m = 15, what is the closest equilibrium position of the bead to the origin? (Give your answer in terms of a.) 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 p are not necessarily integers. (Give your answer as an inequality. Use the following as necessary: m, n, p.)
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