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Given that D= (10x³/3)x C/m², evaluate both sides of the divergence theorem for the volume of a cube, 2 m per edge, centered at the origin and with edges parallel to the axes.

Given that D= (10x³/3)x C/m², evaluate both sides of the divergence theorem for the volume of a cube, 2 m per edge, centered at the origin and with edges parallel to the axes.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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**Problem Statement:** Given that \( D = \left(\frac{10x^3}{3}\right) \hat{x} \ \text{C/m}^2 \), evaluate both sides of the divergence theorem for the volume of a cube, 2 m per edge, centered at the origin and with edges parallel to the axes. **Explanation:** The vector field \( D \) is expressed as \( D = \left(\frac{10x^3}{3}\right) \hat{x} \ \text{C/m}^2 \), where \( \hat{x} \) is the unit vector in the x-direction. This problem involves applying the divergence theorem to a cube in a three-dimensional space. The cube is defined with sides of 2 meters each, centered at the origin (0,0,0), meaning each vertex of the cube ranges from -1 to 1 along the x, y, and z axes, respectively. You should compute the surface integral of \( D \) over the surface of the cube and the volume integral of the divergence of \( D \) over the volume of the cube. The divergence theorem states that these two values should be equal. Note: There are no graphs or diagrams included in this text.
Transcribed Image Text:**Problem Statement:** Given that \( D = \left(\frac{10x^3}{3}\right) \hat{x} \ \text{C/m}^2 \), evaluate both sides of the divergence theorem for the volume of a cube, 2 m per edge, centered at the origin and with edges parallel to the axes. **Explanation:** The vector field \( D \) is expressed as \( D = \left(\frac{10x^3}{3}\right) \hat{x} \ \text{C/m}^2 \), where \( \hat{x} \) is the unit vector in the x-direction. This problem involves applying the divergence theorem to a cube in a three-dimensional space. The cube is defined with sides of 2 meters each, centered at the origin (0,0,0), meaning each vertex of the cube ranges from -1 to 1 along the x, y, and z axes, respectively. You should compute the surface integral of \( D \) over the surface of the cube and the volume integral of the divergence of \( D \) over the volume of the cube. The divergence theorem states that these two values should be equal. Note: There are no graphs or diagrams included in this text.
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