The figure shows a spherical shell with uniform volume charge density ρ = 2.06 nC/m3, inner radius a = 8.90 cm, and outer radius b = 3.8a. What is the magnitude of the electric field at radial distances (a) r = 0; (b) r = a/2.00, (c) r = a, (d) r = 1.50a, (e) r = b, and (f) r = 3.00b? ### Diagram Explanation: Charged Conducting Spherical Shell This diagram represents a cross-section of a charged conducting spherical shell. The main components of the diagram are:1. **Inner Sphere:** - The inner sphere is shown as a solid blue circle. - It has a radius labeled as \( a \). - This inner region is uncharged or neutral as it is not shown with any specific charge indication.2. **Outer Shell:** - Surrounding the inner sphere is a spherical shell depicted with a blue annular ring. - The outer shell is dotted with plus signs (+) indicating that it is uniformly positively charged. - The outer shell has an outer radius labeled as \( b \).This configuration is typical in electrostatics problems, where a conductor with a hollow cavity (the inner sphere) is encased within another conductor (the spherical shell). The charges are usually free to move within the conductor of the outer shell and will distribute themselves on the outer surface due to repulsive forces. As a result, the region inside the shell but outside the inner cavity may remain neutral if there are no charges placed inside.### Key Concepts:- **Gauss's Law:** Gauss's Law is often applied to such problems. For a point inside the inner sphere, the electric field is zero due to the symmetric charge distribution. - **Electrostatic Shielding:** The inner sphere is shielded from electric fields present outside the shell, a principle known as electrostatic shielding.For educational purposes, this diagram helps in understanding concepts such as charge distribution, electric field calculations, and the behavior of conductors in electrostatic equilibrium.

The figure shows a spherical shell with uniform volume charge density ρ = 2.06 nC/m3, inner radius a = 8.90 cm, and outer radius b = 3.8a. What is the magnitude of the electric field at radial distances (a) r = 0; (b) r = a/2.00, (c) r = a, (d) r = 1.50a, (e) r = b, and (f) r = 3.00b?

The figure shows a spherical shell with uniform volume charge density ρ = 2.06 nC/m3, inner radius a = 8.90 cm, and outer radius b = 3.8a. What is the magnitude of the electric field at radial distances (a) r = 0; (b) r = a/2.00, (c) r = a, (d) r = 1.50a, (e) r = b, and (f) r = 3.00b?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter25: Gauss’s Law

Section: Chapter Questions

Problem 43PQ: The nonuniform charge density of a solid insulating sphere of radius R is given by = cr2 (r R),...

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Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

The figure shows a spherical shell with uniform volume charge density ρ = 2.06 nC/m³, inner radius a = 8.90 cm, and outer radius b = 3.8a. What is the magnitude of the electric field at radial distances (a) r = 0; (b) r = a/2.00, (c) r = a, (d) r = 1.50a, (e) r = b, and (f) r = 3.00b?

### Diagram Explanation: Charged Conducting Spherical Shell

This diagram represents a cross-section of a charged conducting spherical shell. The main components of the diagram are:

1. **Inner Sphere:**
- The inner sphere is shown as a solid blue circle.
- It has a radius labeled as \( a \).
- This inner region is uncharged or neutral as it is not shown with any specific charge indication.

2. **Outer Shell:**
- Surrounding the inner sphere is a spherical shell depicted with a blue annular ring.
- The outer shell is dotted with plus signs (+) indicating that it is uniformly positively charged.
- The outer shell has an outer radius labeled as \( b \).

This configuration is typical in electrostatics problems, where a conductor with a hollow cavity (the inner sphere) is encased within another conductor (the spherical shell). The charges are usually free to move within the conductor of the outer shell and will distribute themselves on the outer surface due to repulsive forces. As a result, the region inside the shell but outside the inner cavity may remain neutral if there are no charges placed inside.

### Key Concepts:

- **Gauss's Law:**
Gauss's Law is often applied to such problems. For a point inside the inner sphere, the electric field is zero due to the symmetric charge distribution.

- **Electrostatic Shielding:**
The inner sphere is shielded from electric fields present outside the shell, a principle known as electrostatic shielding.

For educational purposes, this diagram helps in understanding concepts such as charge distribution, electric field calculations, and the behavior of conductors in electrostatic equilibrium.

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