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 xo distance from its center? (Consider that the surface of the plate lies in the yz plane)

University Physics Volume 2
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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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QUESTION 3
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 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/
)(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/
)(x0
We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to obtain
Transcribed Image Text:QUESTION 3 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 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/ )(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/ )(x0 We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to obtain
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
E =
4 TE,R? Xo (x3 + R²)*/2
Xo (x3 + 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: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 E = 4 TE,R? Xo (x3 + R²)*/2 Xo (x3 + 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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