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(а) Find expressions for the total electric potential at the origin (z = 0), at the center of the ring at z = R, and at a point on the z axis a distance z, from the origin, where 0

(а) Find expressions for the total electric potential at the origin (z = 0), at the center of the ring at z = R, and at a point on the z axis a distance z, from the origin, where 0

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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Transcribe the image as if this text will appear on an Educational website. If there are any graphs or diagrams explain them in detail. --- **Electric Potential and Motion of a Charged Bead** Consider two charged rings with radius \( R \) (uniformly distributed). These rings are located at \( z = R \) and \( z = -R \) along the same \( z \)-axis. **(a)** Find expressions for the total electric potential at the origin (\( z = 0 \)), at the center of the ring at \( z = R \), and at a point on the \( z \)-axis a distance \( z_0 \) from the origin, where \( 0 < z_0 < R \). **(b)** A small bead of mass \( m \) with charge \( q \) is threaded on a frictionless string along the \( z \)-axis. If the bead is released from rest at \( z_0 \), will it move toward the origin or toward the ring at \( z = R \)? **(c)** Find an expression for the speed of the bead as it passes through the point you picked in (b).
Transcribed Image Text:Transcribe the image as if this text will appear on an Educational website. If there are any graphs or diagrams explain them in detail. --- **Electric Potential and Motion of a Charged Bead** Consider two charged rings with radius \( R \) (uniformly distributed). These rings are located at \( z = R \) and \( z = -R \) along the same \( z \)-axis. **(a)** Find expressions for the total electric potential at the origin (\( z = 0 \)), at the center of the ring at \( z = R \), and at a point on the \( z \)-axis a distance \( z_0 \) from the origin, where \( 0 < z_0 < R \). **(b)** A small bead of mass \( m \) with charge \( q \) is threaded on a frictionless string along the \( z \)-axis. If the bead is released from rest at \( z_0 \), will it move toward the origin or toward the ring at \( z = R \)? **(c)** Find an expression for the speed of the bead as it passes through the point you picked in (b).
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Solution:

a)
charge at the center is = q
Potential at center due to this charge element is given by-
 
 
Every point on ring is at distance  from point O and
 
 
 
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