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)
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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 \(b\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F099a9854-7cc3-46b9-a37c-ec0486b4a12a%2F1738f127-5091-4d10-8e54-5b2f3ccf3eab%2Fccce9w_processed.png&w=3840&q=75)
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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