A uniform charge density of 53 nC/m3 is distributed throughout a spherical volume (radius = 16.8 cm). Consider a cubical (4.3 cm along the edge) surface completely inside the sphere. Determine the electric flux through this surface. **Title: Understanding 3D Shapes: Intersection of a Cube and a Sphere****Introduction:**In this lesson, we will explore the fascinating intersection of basic 3D shapes: a cube and a sphere. By understanding how these shapes can coexist and intersect within the same space, we can deepen our grasp of spatial relationships and geometric properties.**Description of the Image:**The image above displays a 3-dimensional visualization where a transparent sphere and a solid cube intersect. The sphere is large enough to fully enclose the cube within it. The following three elements are key to understanding this illustration:1. **Sphere:** - The sphere is represented by a large, semi-transparent, gray object. This transparency allows us to see the red cube inside the sphere. - The sphere is centered on the same point as the cube, ensuring that the cube remains wholly inside the sphere. - The uniform grid lines on the base plane help in understanding the proportional dimensions of the sphere.2. **Cube:** - The cube is depicted as a solid red shape. - All edges of the cube are visible through the sphere, indicating that the cube is entirely contained within the sphere. - The base of the cube aligns with the grid on the base plane, which is helpful in recognizing the dimensions and orientation of the cube. 3. **Grid Plane:** - The grid plane is a flat, light blue surface with a checkered pattern, providing a reference for scale and orientation. - The grid lines help decipher the alignment and proportional sizes of both the cube and the sphere in 3D space.**Analysis:**- **Intersection Properties:** - The sphere and the cube intersect in such a way that the entire volume of the cube is contained within the volume of the sphere. - Visualizing and identifying such intersections aids in understanding concepts of volume and surface area in a more intuitive way.- **Practical Applications:** - This kind of geometric understanding is fundamental in fields like computer graphics, architectural design, and various engineering disciplines. Comprehending how different shapes interact and occupy space can lead to more efficient design and structural integrity.**Conclusion:**This image provides a clear and efficient way to visualize how a cube fits within a sphere. By analyzing such geometric intersections, we gain valuable insights into the properties and spatial relationships of 3D shapes. Keep practicing with different geometric configurations to enhance your spatial awareness and geometric

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A uniform charge density of 53 nC/m3 is distributed throughout a spherical volume (radius = 16.8 cm). Consider a cubical (4.3 cm along the edge) surface completely inside the sphere. Determine the electric flux through this surface.

A uniform charge density of 53 nC/m3 is distributed throughout a spherical volume (radius = 16.8 cm). Consider a cubical (4.3 cm along the edge) surface completely inside the sphere. Determine the electric flux through this surface.

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

A uniform charge density of 53 nC/m³ is distributed throughout a spherical volume (radius = 16.8 cm). Consider a cubical (4.3 cm along the edge) surface completely inside the sphere. Determine the electric flux through this surface.

**Title: Understanding 3D Shapes: Intersection of a Cube and a Sphere**

**Introduction:**
In this lesson, we will explore the fascinating intersection of basic 3D shapes: a cube and a sphere. By understanding how these shapes can coexist and intersect within the same space, we can deepen our grasp of spatial relationships and geometric properties.

**Description of the Image:**

The image above displays a 3-dimensional visualization where a transparent sphere and a solid cube intersect. The sphere is large enough to fully enclose the cube within it. The following three elements are key to understanding this illustration:

1. **Sphere:**
- The sphere is represented by a large, semi-transparent, gray object. This transparency allows us to see the red cube inside the sphere.
- The sphere is centered on the same point as the cube, ensuring that the cube remains wholly inside the sphere.
- The uniform grid lines on the base plane help in understanding the proportional dimensions of the sphere.

2. **Cube:**
- The cube is depicted as a solid red shape.
- All edges of the cube are visible through the sphere, indicating that the cube is entirely contained within the sphere.
- The base of the cube aligns with the grid on the base plane, which is helpful in recognizing the dimensions and orientation of the cube.

3. **Grid Plane:**
- The grid plane is a flat, light blue surface with a checkered pattern, providing a reference for scale and orientation.
- The grid lines help decipher the alignment and proportional sizes of both the cube and the sphere in 3D space.

**Analysis:**

- **Intersection Properties:**
- The sphere and the cube intersect in such a way that the entire volume of the cube is contained within the volume of the sphere.
- Visualizing and identifying such intersections aids in understanding concepts of volume and surface area in a more intuitive way.

- **Practical Applications:**
- This kind of geometric understanding is fundamental in fields like computer graphics, architectural design, and various engineering disciplines. Comprehending how different shapes interact and occupy space can lead to more efficient design and structural integrity.

**Conclusion:**

This image provides a clear and efficient way to visualize how a cube fits within a sphere. By analyzing such geometric intersections, we gain valuable insights into the properties and spatial relationships of 3D shapes. Keep practicing with different geometric configurations to enhance your spatial awareness and geometric

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