A thin ring of radius R and uniformly distributed total charge q is located in the xy-plane with its center at the origin. (a) (5 stig) Show that the electric potential on the central axis (the z-axis) of a distance z from the rings center is given by, V = 1 9 4π€о √R² +2² (b) (5 stig) Using this result, derive an expression for the electric field at any point along the z-axis.

A thin ring of radius R and uniformly distributed total charge q is located in the xy-plane with its center at the origin. (a) (5 stig) Show that the electric potential on the central axis (the z-axis) of a distance z from the rings center is given by, V = 1 9 4π€о √R² +2² (b) (5 stig) Using this result, derive an expression for the electric field at any point along the z-axis.

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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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 thin ring of radius R and uniformly distributed total charge q is located in the xy-plane
with its center at the origin.
(a) (5 stig) Show that the electric potential on the central axis (the z-axis) of a distance z
from the rings center is given by,
V =
1
q
4π€о √R² + 2²
(b) (5 stig) Using this result, derive an expression for the electric field at any point along
the z-axis.

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