### Electric Field in a Cube**Description:**A cube with an edge length of 0.47 meters is positioned with one corner at the origin of a Cartesian coordinate system. The edges of the cube align with the x, y, and z axes. In this region of space, the electric field is oriented parallel to the z-axis.**Electric Field Details:**- At the top of the cube (z = 0.47 m), the electric field is: \[ \vec{E} = 1200 \hat{k} \, \text{N/C} \]- At the bottom of the cube (z = 0 m), the electric field is: \[ \vec{E} = 600 \hat{k} \, \text{N/C} \]The task is to determine the net charge contained within the cube.**Diagram Explanation:**The diagram shows a cube with its edges aligned along the x, y, and z axes. The electric field vectors (\(\vec{E}\)) are depicted with arrows pointing along the z-axis, upwards and downwards through the top and bottom faces of the cube, respectively. The \(\hat{k}\) notation represents the unit vector in the z-direction.**Problem:**Calculate the net charge contained within the cube.This configuration and the differences in the electric field at the top and bottom of the cube suggest the use of Gauss's law to find the net charge enclosed within the cube.

Answered: Image /qna-images/answer/94759453-9c57-4a94-b189-add40d081a12.jpg

(at z Ē A cube that is 0.47 m on an edge is oriented with one corner at the origin and three edges along the axes of a Cartesian coordinate system. The electric field in this region of space is parallel to the z-axis. The electric field at the top of the cube 0.47 m) is Ē 1200 N/C. The electric field at the bottom of the cube (at z = 0 m) is Ē – 600k N/C. = = How much net charge is contained within the cube? = Y

(at z Ē A cube that is 0.47 m on an edge is oriented with one corner at the origin and three edges along the axes of a Cartesian coordinate system. The electric field in this region of space is parallel to the z-axis. The electric field at the top of the cube 0.47 m) is Ē 1200 N/C. The electric field at the bottom of the cube (at z = 0 m) is Ē – 600k N/C. = = How much net charge is contained within the cube? = Y

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

### Electric Field in a Cube

**Description:**

A cube with an edge length of 0.47 meters is positioned with one corner at the origin of a Cartesian coordinate system. The edges of the cube align with the x, y, and z axes. In this region of space, the electric field is oriented parallel to the z-axis.

**Electric Field Details:**

- At the top of the cube (z = 0.47 m), the electric field is:

\[
\vec{E} = 1200 \hat{k} \, \text{N/C}
\]

- At the bottom of the cube (z = 0 m), the electric field is:

\[
\vec{E} = 600 \hat{k} \, \text{N/C}
\]

The task is to determine the net charge contained within the cube.

**Diagram Explanation:**

The diagram shows a cube with its edges aligned along the x, y, and z axes. The electric field vectors (\(\vec{E}\)) are depicted with arrows pointing along the z-axis, upwards and downwards through the top and bottom faces of the cube, respectively. The \(\hat{k}\) notation represents the unit vector in the z-direction.

**Problem:**

Calculate the net charge contained within the cube.

This configuration and the differences in the electric field at the top and bottom of the cube suggest the use of Gauss's law to find the net charge enclosed within the cube.

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