### Educational Website Transcription---#### Problem 3**Description:**A hollow copper spherical shell with an inner radius \( a = 2 \, \text{cm} \) and an outer radius \( b = 3 \, \text{cm} \) carries a charge of \(- 1.6 \, \mu \text{C}\). At the center of the sphere, there is a positive point charge of \( +10 \, \mu \text{C} \). Find an expression for the electric field \( E(r) \) in the three regions I, II, and III, where \( r \) is the distance from the center. Include the direction in your answers.**Diagram Explained:** The diagram features a cross-sectional view of the spherical shell divided into three labeled regions. - Region I is within the inner radius \( (r < a) \).- Region II is between the inner and outer radii \( (a < r < b) \).- Region III is outside the outer radius \( (r > b) \).Arrows point radially outward from the center, indicating the direction of the electric field.---#### Problem 4**Description:**- **Part a:** The point charge is at the center of a cube. The cube has sides of \( 1 \, \text{cm} \) and \( 1.5 \, \text{cm} \). Find first the electric flux through the side of the cube that is facing a cone, and then the total flux through the cone with a height of \( 2 \, \text{cm} \) and radius \( 0.8 \, \text{cm} \). **Diagram Explained:** A cube with a point charge \( +10 \, \mu \text{C} \) at its center adjacent to a cone is illustrated. The dimensions of the cube's side (\( 1 \, \text{cm} \) and \( 1.5 \, \text{cm} \)) and the cone's height (\( 2 \, \text{cm} \)) and base radius (\( 0.8 \, \text{cm} \)) are provided.- **Part b:** Remove the cube and the point charge. Assume now there is a uniform vertical electric field \( E =

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3) A hollow copper spherical shell of inner radius a = 2 cm and outer radius b = 3 cm carries a charge of - 16 micro C. At the center of the sphere there is a positive point charge. Find an expression for the electric field E(r) in the three regions I, II, and III, where r is the distance from the center. Include the direction in your answers. + 10 u C ain copper ain

3) A hollow copper spherical shell of inner radius a = 2 cm and outer radius b = 3 cm carries a charge of - 16 micro C. At the center of the sphere there is a positive point charge. Find an expression for the electric field E(r) in the three regions I, II, and III, where r is the distance from the center. Include the direction in your answers. + 10 u C ain copper ain

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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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

### Educational Website Transcription

---

#### Problem 3
**Description:**

A hollow copper spherical shell with an inner radius \( a = 2 \, \text{cm} \) and an outer radius \( b = 3 \, \text{cm} \) carries a charge of \(- 1.6 \, \mu \text{C}\). At the center of the sphere, there is a positive point charge of \( +10 \, \mu \text{C} \). Find an expression for the electric field \( E(r) \) in the three regions I, II, and III, where \( r \) is the distance from the center. Include the direction in your answers.

**Diagram Explained:**

The diagram features a cross-sectional view of the spherical shell divided into three labeled regions.
- Region I is within the inner radius \( (r < a) \).
- Region II is between the inner and outer radii \( (a < r < b) \).
- Region III is outside the outer radius \( (r > b) \).

Arrows point radially outward from the center, indicating the direction of the electric field.

---

#### Problem 4
**Description:**

- **Part a:**

The point charge is at the center of a cube. The cube has sides of \( 1 \, \text{cm} \) and \( 1.5 \, \text{cm} \). Find first the electric flux through the side of the cube that is facing a cone, and then the total flux through the cone with a height of \( 2 \, \text{cm} \) and radius \( 0.8 \, \text{cm} \).

**Diagram Explained:**

A cube with a point charge \( +10 \, \mu \text{C} \) at its center adjacent to a cone is illustrated. The dimensions of the cube's side (\( 1 \, \text{cm} \) and \( 1.5 \, \text{cm} \)) and the cone's height (\( 2 \, \text{cm} \)) and base radius (\( 0.8 \, \text{cm} \)) are provided.

- **Part b:**

Remove the cube and the point charge. Assume now there is a uniform vertical electric field \( E =

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