Problem Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius Rand total charge Q) at xo distance from its center? (Consider that the surface of the plate lies in the yz plane) 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/ 2,2) Since, the actual ring (whose charge is dq) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as 2. = (1/ Xx0 We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to obtain .R E- (x0/ Evaluating the integral will lead us to Qxo E=- 4 TEGR? Xo (x3 + R?)=/2 1 1 For the case where in R is extremely bigger than x0. Without other substitutions, the equation above will reduce to E= Q/ Eg)

Problem Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius Rand total charge Q) at xo distance from its center? (Consider that the surface of the plate lies in the yz plane) 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/ 2,2) Since, the actual ring (whose charge is dq) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as 2. = (1/ Xx0 We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to obtain .R E- (x0/ Evaluating the integral will lead us to Qxo E=- 4 TEGR? Xo (x3 + R?)=/2 1 1 For the case where in R is extremely bigger than x0. Without other substitutions, the equation above will reduce to E= Q/ Eg)

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter5: Electric Charges And Fields

Section: Chapter Questions

Problem 101P: In this exercise, you practice electric field lines. Make sure you represent both the magnitude and...

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