A thin line charge, infinite in both directions, has a charge density per unit length ^ of 2.00 µC/m. What is the electric field strength a distance 0.50 meters from the line! a. 入 3.8 X1CA RTI( 8.85x1019) cosec tion: ヤート
A thin line charge, infinite in both directions, has a charge density per unit length ^ of 2.00 µC/m. What is the electric field strength a distance 0.50 meters from the line! a. 入 3.8 X1CA RTI( 8.85x1019) cosec tion: ヤート
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)...
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![**Educational Website Transcription and Explanation**
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**Problem A: Electric Field from a Line Charge**
A thin line charge, infinite in both directions, has a charge density per unit length \( \lambda \) of 2.00 \(\mu\text{C/m}\). What is the electric field strength at a distance of 0.50 meters from the line charge?
\[ E = \frac{\lambda}{2\pi\varepsilon_0} = \frac{(2 \times 10^{-6})}{2\pi (8.85 \times 10^{-12})} = 3.8 \times 10^4 \]
*Correction noted: replace \(\pi\) with \(x-1\) in the denominator.*
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**Problem B: Electrostatic Force on a Charge**
A \(-5.00 \, \mu\text{C}\) charge is 0.50 meters from the line charge mentioned in part A. What is the electrostatic force on this charge? Is this force directed toward or away from the line charge?
\[ F = EQ = (3.8 \times 10^4)(-5 \times 10^{-6}) = -0.19 \]
The force is negative, indicating it is directed toward the line charge.
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**Problem C: Electric Field from a Charged Membrane**
A large flat insulating membrane has a uniform charge \( \sigma \) of \( 12.0 \, \mu\text{C/m}^2 \). What is the electric field strength above the charged surface?
\[ E = \frac{\sigma}{2\varepsilon_0} = \frac{12 \times 10^{-6}}{2(8.85 \times 10^{-12})} = 5.31 \times 10^7 \]
*Comment noted: electric field would double with \(x-4\).*
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**Problem D: Electric Field from Two Charges**
Suppose a \( +4.00 \, \mu\text{C} \) charge and a \( +7.00 \, \mu\text{C} \) charge are separated by 3.00 meters. How far from the \( +4.00 \, \mu\text{C} \) charge does the electric field vanish? What is the magnitude of the force on a test charge if it is placed at](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F15f07b92-5703-4de4-9426-36c09b5d48af%2Fdb0b8da8-5bef-4e29-9a41-7c2e886a5a52%2F8wdlmyk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Transcription and Explanation**
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**Problem A: Electric Field from a Line Charge**
A thin line charge, infinite in both directions, has a charge density per unit length \( \lambda \) of 2.00 \(\mu\text{C/m}\). What is the electric field strength at a distance of 0.50 meters from the line charge?
\[ E = \frac{\lambda}{2\pi\varepsilon_0} = \frac{(2 \times 10^{-6})}{2\pi (8.85 \times 10^{-12})} = 3.8 \times 10^4 \]
*Correction noted: replace \(\pi\) with \(x-1\) in the denominator.*
---
**Problem B: Electrostatic Force on a Charge**
A \(-5.00 \, \mu\text{C}\) charge is 0.50 meters from the line charge mentioned in part A. What is the electrostatic force on this charge? Is this force directed toward or away from the line charge?
\[ F = EQ = (3.8 \times 10^4)(-5 \times 10^{-6}) = -0.19 \]
The force is negative, indicating it is directed toward the line charge.
---
**Problem C: Electric Field from a Charged Membrane**
A large flat insulating membrane has a uniform charge \( \sigma \) of \( 12.0 \, \mu\text{C/m}^2 \). What is the electric field strength above the charged surface?
\[ E = \frac{\sigma}{2\varepsilon_0} = \frac{12 \times 10^{-6}}{2(8.85 \times 10^{-12})} = 5.31 \times 10^7 \]
*Comment noted: electric field would double with \(x-4\).*
---
**Problem D: Electric Field from Two Charges**
Suppose a \( +4.00 \, \mu\text{C} \) charge and a \( +7.00 \, \mu\text{C} \) charge are separated by 3.00 meters. How far from the \( +4.00 \, \mu\text{C} \) charge does the electric field vanish? What is the magnitude of the force on a test charge if it is placed at
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