A ring of radius R that lies in the xy plane carries a positive charge Q uniformly distributed over its length. A particle of mass m that carries a negative charge of magnitude q is at the center of the ring. (a) Show that if x «R, the electric field along the axis of the ring is proportional to z. (b) Find the force on the particle of mass m as a function of z. (c) Show that if m is given a small displacement in the x direction, it will perform simple harmonic motion. Calculate the period of that motion

A ring of radius R that lies in the xy plane carries a positive charge Q uniformly distributed over its length. A particle of mass m that carries a negative charge of magnitude q is at the center of the ring. (a) Show that if x «R, the electric field along the axis of the ring is proportional to z. (b) Find the force on the particle of mass m as a function of z. (c) Show that if m is given a small displacement in the x direction, it will perform simple harmonic motion. Calculate the period of that motion

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

A ring of radius R that lies in the xy plane carries a positive charge Q
uniformly distributed over its lerigth. A particle of mass m that carries a
negative charge of magnitude q is at the center of the ring. (a) Show that if x
<< R, the electric field along the axis of the ring is proportional to z. (b) Find
the force on the particle of mass m as a function of z. (c) Show that if m is
given a small displacement in the x direction, it will perform simple
harmonic motion. Calculate the period of that motion

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Step 1: Introduce the consideration

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Step 2: Calculate the potential at a distance z from centre

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Step 3: Calculate the electric field at the distance z from centre

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Step 4: Calculate the force on charge -q

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Step 5: Calculate the time period of simple harmonic motion

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