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Show that the electric filed at a location on the x axis, a distance l from the origin comes out to be 2nkeR =- (P+R2)3/2

Show that the electric filed at a location on the x axis, a distance l from the origin comes out to be 2nkeR =- (P+R2)3/2

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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Question 5: Consider the following situation: A ring of radius R is centered on the x axis a distance l from the origin. The ring has a uniform electric charge density per unit length d, d > 0. Show that the electric filed at a location on the x axis, a distance l from the origin comes out to be Ē = 2nkeAlR (?+ R?}3/2 Hint: You will need to set up an integration for this problem.
Transcribed Image Text:Question 5: Consider the following situation: A ring of radius R is centered on the x axis a distance l from the origin. The ring has a uniform electric charge density per unit length d, d > 0. Show that the electric filed at a location on the x axis, a distance l from the origin comes out to be Ē = 2nkeAlR (?+ R?}3/2 Hint: You will need to set up an integration for this problem.
Expert Solution
Step 1

Analyze the following figure.

Physics homework question answer, step 1, image 1

The electric field’s components in the Z direction will get cancel out due to the symmetry of the ring. Thus, the net electric field at P is only due to the field’s X-components.

The electric field at the point P can be represented as,

Physics homework question answer, step 1, image 2

Here, ke, dq, x, and θ represent the Coulomb’s law constant, the small charge, the point’s distance from the line element, and the angle that the electric field makes with X-axis, respectively.

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