4) Electric field of a rod. Consider a nonconducting rod of length L with a charge q uniformly distributed along its length. We want to know the magnitude of the electric field a distance x away from one end as shown below. L, with q evenly distributed Explain why EACH of the four answers below is WRONG. Consider symmetry, dimensions, unit analysis, behavior in limiting cases, and/or behavior at particular positions. You SHOULD NOT actually solve the problem and your answer shouldn’t be because the correct answer is this. This is good practice in considering the nature of your answer.. a) E = b) E = Απε, L (x + L) ΑπεοX(x-L) c) E = d) E = Απε, (x + LI4) 4tɛ,x(2x+ L)

Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
icon
Related questions
Question
4) Electric field of a rod. Consider a nonconducting rod of length L with a charge q
uniformly distributed along its length. We want to know the magnitude of the electric
field a distance x away from one end as shown below.
X
L, with q evenly distributed
Explain why EACH of the four answers below is WRONG. Consider symmetry,
dimensions, unit analysis, behavior in limiting cases, and/or behavior at particular
positions. You SHOULD NOT actually solve the problem and your answer shouldn't be
because the correct answer is this. This is good practice in considering the nature of your
answer...
а) Е:
b) E =
4πε, L(x + L)
4TE,x(x – L)
c) E =
d) E =
4л, (х? + L/4)
4лєрх(2х + L)
5) Electric field of a rod again--this time with calculus and a different geometry
•Part a: A thin nonconducting rod of length L has charge q uniformly distributed along it
as shown in Fig. 22-55 (associated with problem 32). SHOW that the magnitude of the
electric field at point P (on the perpendicular bisector of the rod) is given by:
1
2 TE,R JĽ² +4R²
If your integral calculus is rusty, you might want to look at Appendix E in your text.
(Again, since I've given you the final form, you must SHOW the steps leading to the
result above.)
•Part b: Justify the functional form of your expression for E, by considering what it
reduces to in the limit of R>>L. Is this expression what you expect? Also find an
expression for the opposite limit of L>>R. We will discuss this shortly in the context of
Gauss' law, so remember what this is!
Transcribed Image Text:4) Electric field of a rod. Consider a nonconducting rod of length L with a charge q uniformly distributed along its length. We want to know the magnitude of the electric field a distance x away from one end as shown below. X L, with q evenly distributed Explain why EACH of the four answers below is WRONG. Consider symmetry, dimensions, unit analysis, behavior in limiting cases, and/or behavior at particular positions. You SHOULD NOT actually solve the problem and your answer shouldn't be because the correct answer is this. This is good practice in considering the nature of your answer... а) Е: b) E = 4πε, L(x + L) 4TE,x(x – L) c) E = d) E = 4л, (х? + L/4) 4лєрх(2х + L) 5) Electric field of a rod again--this time with calculus and a different geometry •Part a: A thin nonconducting rod of length L has charge q uniformly distributed along it as shown in Fig. 22-55 (associated with problem 32). SHOW that the magnitude of the electric field at point P (on the perpendicular bisector of the rod) is given by: 1 2 TE,R JĽ² +4R² If your integral calculus is rusty, you might want to look at Appendix E in your text. (Again, since I've given you the final form, you must SHOW the steps leading to the result above.) •Part b: Justify the functional form of your expression for E, by considering what it reduces to in the limit of R>>L. Is this expression what you expect? Also find an expression for the opposite limit of L>>R. We will discuss this shortly in the context of Gauss' law, so remember what this is!
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 3 images

Blurred answer
Knowledge Booster
Routh Hurwitz Criteria
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,