You have a summer intern position with a company that designs and builds nanoma- chines. An engincer with the company is designing a microscopic oscillator to help keep time, and you've been assigned to help him analyze the design. He wants to place a negative charge at the center of a very small, positively charged metal loop. His claim is that the negative charge will undergo simple harmonic motion at a frequency determined by the amount of charge on the loop. (a) Consider a negative charge near the center of a positively charged ring. Show that there is a restoring force on the charge if it moves along the z-axis but stays close to the center. That is, show there's a force that tires to keep the charge at z = 0. (b) Show that for small oscillations, with amplitude < R, a particle of mass m with charge -q undergoes simple harmonic motion with frequency 1 2n V 4T€omR3 R and Q are the radius and charge of the ring. (c) Evaluate the oscillation frequency for an clectron at the center of a 2.0 um- diameter ring charged to 1.0 × 10–13 C.

You have a summer intern position with a company that designs and builds nanoma- chines. An engincer with the company is designing a microscopic oscillator to help keep time, and you've been assigned to help him analyze the design. He wants to place a negative charge at the center of a very small, positively charged metal loop. His claim is that the negative charge will undergo simple harmonic motion at a frequency determined by the amount of charge on the loop. (a) Consider a negative charge near the center of a positively charged ring. Show that there is a restoring force on the charge if it moves along the z-axis but stays close to the center. That is, show there's a force that tires to keep the charge at z = 0. (b) Show that for small oscillations, with amplitude < R, a particle of mass m with charge -q undergoes simple harmonic motion with frequency 1 2n V 4T€omR3 R and Q are the radius and charge of the ring. (c) Evaluate the oscillation frequency for an clectron at the center of a 2.0 um- diameter ring charged to 1.0 × 10–13 C.

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter19: Electric Forces And Electric Fields

Section: Chapter Questions

Problem 76P

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