3. Let F(r, y, z) = 3zi – 2y3 – (x + y) k. For each of the surfaces in Parts (a)-(d), say whether the flux of Fthrough the surface is positive, negative, or zero. In cach case, the orientation of the surface is indicated bythe given normal vector.(a)(b)(c)(d)

Answered: Let F(r, y, 2) = 3z7- 2y 3 – (x + y) E.…

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 7CQ: (a) If the electric flux through a closed surface is zero, is the electric field necessarily zero at...

See similar textbooks

Related questions

Concept explainers

Question

100%

3. Let F(r, y, z) = 3zi – 2y3 – (x + y) k. For each of the surfaces in Parts (a)-(d), say whether the flux of F
through the surface is positive, negative, or zero. In cach case, the orientation of the surface is indicated by
the given normal vector.
(a)
(b)
(c)
(d)

Expert Solution

Step 1

Hi. Since you have posted a question with multiple subparts and not specified which subparts you want us to solve, we will solve the first three subparts for you. If you want the remaining subpart to be answered, please resubmit the question and specify the subpart that needs to be solved.

The flux (φ) of a vector field (F) through an area (A) can be calculated as follows:

$φ = \int_{A}^{} \vec{F} \cdot \vec{d A}$

Here, dA is the vector area element.

Step 2

(a)

The area element (dA_a = dydz) in the diagram is along the positive x-axis. The unit vector (i) is along the positive x-axis. The plane has the limits (y > 0, z > 0).

Determine the flux (φ_a) in this case in the integral form to check its sign as follows:

$\begin{array}{rcl} φ_{a} & = & \int \vec{F} \cdot \vec{d A_{a}} \\ = & \int_{y > 0, z > 0}^{} (3 z \hat{i} - 2 y \hat{j} - (x + y) \hat{k}) \cdot (d y d z \hat{i}) \\ = & \int_{y > 0}^{} d y \int_{z > 0}^{} 3 z d z \\ > & 0 \end{array}$

Hence, the flux in this case is positive.

Step by step

Solved in 4 steps

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

SEE MORE QUESTIONS

Recommended textbooks for you

University Physics Volume 2

Physics

ISBN:

9781938168161

Author:

OpenStax

Publisher:

OpenStax

Principles of Physics: A Calculus-Based Text

Physics

ISBN:

9781133104261

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

University Physics Volume 2

Physics

ISBN:

9781938168161

Author:

OpenStax

Publisher:

OpenStax

Principles of Physics: A Calculus-Based Text

Physics

ISBN:

9781133104261

Author:

Raymond A. Serway, John W. Jewett

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Let F(r, y, 2) = 3z7- 2y 3 – (x + y) E. For each of the surfaces in Parts (a)-(d), say whether the flux of F through the surface is positive, negative, or zero. In each case, the orientation of the surface is indicated by the given normal vector. (a) (b) (c) (d)