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Compute the gradient and Laplacian of the function T = r

Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths ISBN: 9780321856562 45

Solution for problem 41P Chapter 1

Introduction to Electrodynamics | 4th Edition

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Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths

Introduction to Electrodynamics | 4th Edition

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Problem 41P

Compute the gradient and Laplacian of the function T = r (cos θ + sin θ cos ϕ). Check the Laplacian by converting T to Cartesian coordinates and using Eq. 1.42. Test the gradient theorem for this function, using the path shown in Fig. 1.41, from (0, 0, 0) to (0, 0, 2).

Eq. 1.42

Step-by-Step Solution:

Problem 41P

Solution 41P

Step 1 of 5:

In this question, we need to find gradient and Laplacian of function

Laplacian needs to be checked in terms of cartesian coordinates

Gradient of the function has be checked using the path given in the figure

Data given

Cartesian coordinates are given as

                        

        

                

 

The figure give

        

        

Step 2 of 5:

We shall find the gradient of the function

We have gradient as

                

Using this on function

We get

                        

Thus we have obtained the gradient of the function

Step 3 of 4

Chapter 1, Problem 41P is Solved
Step 4 of 4

Textbook: Introduction to Electrodynamics
Edition: 4
Author: David J. Griffiths
ISBN: 9780321856562

The answer to “Compute the gradient and Laplacian of the function T = r (cos ? + sin ? cos ?). Check the Laplacian by converting T to Cartesian coordinates and using Eq. 1.42. Test the gradient theorem for this function, using the path shown in Fig. 1.41, from (0, 0, 0) to (0, 0, 2).Eq. 1.42” is broken down into a number of easy to follow steps, and 54 words. This textbook survival guide was created for the textbook: Introduction to Electrodynamics , edition: 4. This full solution covers the following key subjects: Using, LaPlacian, cos, function, gradient. This expansive textbook survival guide covers 12 chapters, and 550 solutions. Introduction to Electrodynamics was written by and is associated to the ISBN: 9780321856562. Since the solution to 41P from 1 chapter was answered, more than 329 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 41P from chapter: 1 was answered by , our top Physics solution expert on 07/18/17, 05:41AM.

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