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.

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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Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

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 forcc on the charge if it moves along the z-axis but stays
close to the center. That is, show there's a force that tircs 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 electron at the center of a 2.0 um-
diameter ring charged to 1.0 x 10 13 C.

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