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Problem Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius R and total charge Q) at x0 distance from its center? (Consider that the surface

Problem Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius R and total charge Q) at x0 distance from its center? (Consider that the surface

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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Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius R and total charge Q) at x0 distance from its center? (Consider that the surface of the plate lies in the yz plane)

QUESTION 6 Problem Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius R and total charge Q) at xn distance from its center? (Consider that the surface of the plate lies in th Solution A perfect approach to this is to first obtain the E-field produced by an infinitesimal charge component of the charge Q. There will be several approaches to do this, but the most familiar to us is to obtain a very small shape that could easily represent our circular plane. That shape would be a ring. So for a ring whose charge is q, we recall that the electric field it produces at distance x0 is given by E = (1/ )(x0qy( 2412) Since, the actual ring (whose charge is dg) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as = (1/ We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to obtain E = (x0/ 24 Evaluating the integral will lead us to Qxo 1 1 4 nER? Xo (x; + R?)+/2 For the case where in R is extremely bigger than x0. Without other substitutions, the equation above will reduce to E = Q/(
Transcribed Image Text:QUESTION 6 Problem Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius R and total charge Q) at xn distance from its center? (Consider that the surface of the plate lies in th Solution A perfect approach to this is to first obtain the E-field produced by an infinitesimal charge component of the charge Q. There will be several approaches to do this, but the most familiar to us is to obtain a very small shape that could easily represent our circular plane. That shape would be a ring. So for a ring whose charge is q, we recall that the electric field it produces at distance x0 is given by E = (1/ )(x0qy( 2412) Since, the actual ring (whose charge is dg) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as = (1/ We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to obtain E = (x0/ 24 Evaluating the integral will lead us to Qxo 1 1 4 nER? Xo (x; + R?)+/2 For the case where in R is extremely bigger than x0. Without other substitutions, the equation above will reduce to E = Q/(
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