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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)

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)
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...
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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!
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