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/ 242) 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 2. = (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/ Evaluating the integral will lead us to Qxo 1 1 E= 4 TEGR? | Xo (x3 + R²)/2 For the case where in Ris extremely bigger than x0. Without other substitutions, the equation above will reduce to E= Q/(
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/ 242) 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 2. = (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/ Evaluating the integral will lead us to Qxo 1 1 E= 4 TEGR? | Xo (x3 + R²)/2 For the case where in Ris extremely bigger than x0. Without other substitutions, the equation above will reduce to E= Q/(
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)...
Related questions
Question
Please fill in the blanks.
Transcribed Image Text: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/
D(x0q)/
24,2)
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/
D(x0
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/
Evaluating the integral will lead us to
QXo
1
1
E=
4 TEGR? Xo (x3 +R²)=/2
For the case where in R is extremely bigger than x0. Without other substitutions, the equation above will reduce to
E= Q
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON