What is the magnitude of electric field at point P, the center of the cube?

College Physics
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Chapter1: Units, Trigonometry. And Vectors
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Consider a regular cube with positive point charge +in all corners except for one which has a negative point charge -Q. Let the distance from any corner to the center of the cube be r. What is the magnitude of electric field at point P, the center of the cube? (options below)

E = 2k Q / r^2
E = 1k Q / r^2
E = 0
E = 7k Q / r^2
E = 6k Q / r^2
The image shows a 3D diagram of a cube with vertices marked by circles. The circles contain plus signs, indicating positive charges. There is one black circle at the vertex in the bottom left corner, contrasting with the others. At the center of the cube, there is a point labeled "P".

**Explanation of the Diagram:**

1. **Structure**: 
   - The diagram represents a cube, which is a three-dimensional shape with six faces, twelve edges, and eight vertices.

2. **Vertices**:
   - Each vertex of the cube is marked with a circle containing a plus sign, except for one black circle. The plus signs likely represent positive charges at these vertices.

3. **Central Point**:
   - The center of the cube contains a point labeled "P", which could represent a position of interest, such as the center of mass, an observation point, or a charge within the cube.

4. **Edges and Faces**:
   - The edges connect the vertices with dashed lines, illustrating the cube’s square faces and spatial dimensions.

This diagram is a useful representation when discussing concepts related to electric fields, potential, and symmetry in physics or chemistry contexts.
Transcribed Image Text:The image shows a 3D diagram of a cube with vertices marked by circles. The circles contain plus signs, indicating positive charges. There is one black circle at the vertex in the bottom left corner, contrasting with the others. At the center of the cube, there is a point labeled "P". **Explanation of the Diagram:** 1. **Structure**: - The diagram represents a cube, which is a three-dimensional shape with six faces, twelve edges, and eight vertices. 2. **Vertices**: - Each vertex of the cube is marked with a circle containing a plus sign, except for one black circle. The plus signs likely represent positive charges at these vertices. 3. **Central Point**: - The center of the cube contains a point labeled "P", which could represent a position of interest, such as the center of mass, an observation point, or a charge within the cube. 4. **Edges and Faces**: - The edges connect the vertices with dashed lines, illustrating the cube’s square faces and spatial dimensions. This diagram is a useful representation when discussing concepts related to electric fields, potential, and symmetry in physics or chemistry contexts.
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