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

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### 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 =
Transcribed Image Text:### 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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