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Practice with Gauss' Law: A long cylinder carries a uniform positive charge density +Pa in the region 0≤r≤a, and a uniform negative charge density -Pb in the region a ≤r≤b. Find the field everywhere. Simplify the result for the case when the system is charge neutral (express your answer in terms of +Pa). -Pb b +Pa a

Practice with Gauss' Law: A long cylinder carries a uniform positive charge density +Pa in the region 0≤r≤a, and a uniform negative charge density -Pb in the region a ≤r≤b. Find the field everywhere. Simplify the result for the case when the system is charge neutral (express your answer in terms of +Pa). -Pb b +Pa a

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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**Practice with Gauss' Law:** A long cylinder carries a uniform positive charge density \(+\rho_a\) in the region \(0 \leq r \leq a\), and a uniform negative charge density \(-\rho_b\) in the region \(a \leq r \leq b\). Find the field everywhere. Simplify the result for the case when the system is charge neutral (express your answer in terms of \(+\rho_a\)). **Diagram Explanation:** The accompanying diagram illustrates a cross-section of a cylindrical system. The cylinder has two regions: 1. The inner region, from the center \(r = 0\) to \(r = a\), is shaded in pink and labeled with a positive charge density \(+\rho_a\). 2. The outer region, from \(r = a\) to \(r = b\), is shaded in blue and labeled with a negative charge density \(-\rho_b\). The diagram visually represents the distribution of charges in the two regions of the cylinder and indicates the boundaries at radius \(a\) and radius \(b\).
Transcribed Image Text:**Practice with Gauss' Law:** A long cylinder carries a uniform positive charge density \(+\rho_a\) in the region \(0 \leq r \leq a\), and a uniform negative charge density \(-\rho_b\) in the region \(a \leq r \leq b\). Find the field everywhere. Simplify the result for the case when the system is charge neutral (express your answer in terms of \(+\rho_a\)). **Diagram Explanation:** The accompanying diagram illustrates a cross-section of a cylindrical system. The cylinder has two regions: 1. The inner region, from the center \(r = 0\) to \(r = a\), is shaded in pink and labeled with a positive charge density \(+\rho_a\). 2. The outer region, from \(r = a\) to \(r = b\), is shaded in blue and labeled with a negative charge density \(-\rho_b\). The diagram visually represents the distribution of charges in the two regions of the cylinder and indicates the boundaries at radius \(a\) and radius \(b\).
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