Q 12. Give an example of a field with ... [FREE SOLUTION]

91影视

Chapter 14: Q 12. (page 1131)

Give an example of a field with positive divergence at (1, 0, 蟺).

Short Answer

Expert verified

$An example of field with positive divergence at (1, 0, 蟺) is, F (x, y, z) = x^{2} i + 3 \sin (y) j + \cos (z) k$

Step by step solution

Step 1. Given information is

Point is (1,0,蟺)

Step 2. Example of field

$If F (x, y, z) = F_{1} (x, y, z) i + F_{2} (x, y, z) j + F_{3} (x, y, z) k is a vector field, then the divergence of the vector field is defined as follows : 鈭� . F = \frac{鈭� F_{1}}{鈭� x} + \frac{鈭� F_{2}}{鈭� y} + \frac{鈭� F_{3}}{鈭� z} Note that value of 鈭� . F is scalar . Consider the following vector field : F (x, y, z) = x^{2} i + 3 \sin (y) j + \cos (z) k The divergence of this vector field will be, 鈭� . F = \frac{鈭� (x^{2})}{鈭� x} + \frac{鈭� (3 \sin (y))}{鈭� y} + \frac{鈭� (\cos z)}{鈭� z} = 2 x + 3 cosy - sinz At the origin, that is, at (x, y, z) = (1, 0, 蟺), the divergence of this vector field will be, 鈭� . F = 2.1 + 3 \cos 0 - \sin 蟺 = 2 + 3 - 0 = 5, which is positive . Therefore, an example of field with positive divergence at (1, 0, 蟺) is, F (x, y, z) = x^{2} i + 3 \sin (y) j + \cos (z) k$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Give an example of a field with positive divergence at (1, 0, 蟺).

Short Answer

Step by step solution

Step 1. Given information is

Step 2. Example of field

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Logic and Functions

Pure Maths

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.