**2) More electric flux and a cube***Taken from another textbook. Consider a cube with sides of length \( a \) and one point charge \( +q \) at the corner of the cube as illustrated below:*![Diagram]Solution:1. **Diagram Explanation:** The diagram shows a cube with sides of length \( a \). A point charge \( +q \) is placed at one of the corners of the cube. There are three arrows indicating the three sides of the cube extending away from the corner where the charge is located.2. a) **Explain why the flux through any of the three sides of the cube not touching the point charge (like the gray shaded one) is given by \( \frac{q}{24 \epsilon_0} \):** To understand the flux through the three sides not touching the point charge, consider a larger cube that completely encloses the charge \( +q \). This larger structure would have eight smaller cubes, each similar to the cube illustrated but sharing the corner with the charge. Since flux distributes evenly and the total flux \( \Phi \) due to charge \( q \) is \( \frac{q}{\epsilon_0} \), the flux through one of the three sides of one smaller cube that doesn't touch the charge is \( \frac{q}{24 \epsilon_0} \).3. b) **Explain why the flux through any of the three sides of the cube touching the point charge is zero:** The flux through any of the three sides of the cube touching the point charge is zero because the electric field passes through the point charge directly at the vertex. Since these sides share the point charge, the electric flux through these sides is not perpendicular to the surface and effectively cancels out any contribution of flux on these sides.**Hint: It will be helpful to make a larger (boxy) structure that completely encloses the charge.**

Answered: Image /qna-images/answer/e678a904-583d-46f7-8818-0276b2b14ea4.jpg

2) More electric flux and a cube Taken from another textbook. Consider a cube with sides of length a and one point charge +q at the corner of the cube as illustrated below: +q a) Explain why the flux through any of the three sides of the cube not touching the point charge (like the gray shaded one) is given by 24€0 b) Explain why the flux through any of the three sides of the cube touching the point charge is zero. Hint: It will be helpful to make a larger (boxy) structure that completely encloses the charge.

2) More electric flux and a cube Taken from another textbook. Consider a cube with sides of length a and one point charge +q at the corner of the cube as illustrated below: +q a) Explain why the flux through any of the three sides of the cube not touching the point charge (like the gray shaded one) is given by 24€0 b) Explain why the flux through any of the three sides of the cube touching the point charge is zero. Hint: It will be helpful to make a larger (boxy) structure that completely encloses the charge.

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

**2) More electric flux and a cube**

*Taken from another textbook. Consider a cube with sides of length \( a \) and one point charge \( +q \) at the corner of the cube as illustrated below:*

![Diagram]

Solution:

1. **Diagram Explanation:**
The diagram shows a cube with sides of length \( a \). A point charge \( +q \) is placed at one of the corners of the cube. There are three arrows indicating the three sides of the cube extending away from the corner where the charge is located.

2. a) **Explain why the flux through any of the three sides of the cube not touching the point charge (like the gray shaded one) is given by \( \frac{q}{24 \epsilon_0} \):**

To understand the flux through the three sides not touching the point charge, consider a larger cube that completely encloses the charge \( +q \). This larger structure would have eight smaller cubes, each similar to the cube illustrated but sharing the corner with the charge. Since flux distributes evenly and the total flux \( \Phi \) due to charge \( q \) is \( \frac{q}{\epsilon_0} \), the flux through one of the three sides of one smaller cube that doesn't touch the charge is \( \frac{q}{24 \epsilon_0} \).

3. b) **Explain why the flux through any of the three sides of the cube touching the point charge is zero:**

The flux through any of the three sides of the cube touching the point charge is zero because the electric field passes through the point charge directly at the vertex. Since these sides share the point charge, the electric flux through these sides is not perpendicular to the surface and effectively cancels out any contribution of flux on these sides.

**Hint: It will be helpful to make a larger (boxy) structure that completely encloses the charge.**

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