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Prove that the curl of a gradient is always zero. Check it

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

Solution for problem 28P 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 28P

Problem 28P

Prove that the curl of a gradient is always zero. Check it for function (b) in Prob. 1.11.

Reference Prob. 1.11.

Find the gradients of the following functions:

(a) f (x, y, z) = x2 + y3 + z4.

(b) f (x, y, z) = x2 y3z4.

(c) f (x, y, z) = ex sin(y) ln(z).

Step-by-Step Solution:

Solution

Step 1 of 4

We need to prove that the curl of a gradient is always zero and check the  curl of a gradient of the function .

The gradient of a function is  is,

Step 2 of 4

Chapter 1, Problem 28P is Solved
Step 3 of 4

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

Since the solution to 28P from 1 chapter was answered, more than 419 students have viewed the full step-by-step answer. Introduction to Electrodynamics was written by and is associated to the ISBN: 9780321856562. This textbook survival guide was created for the textbook: Introduction to Electrodynamics , edition: 4. The full step-by-step solution to problem: 28P from chapter: 1 was answered by , our top Physics solution expert on 07/18/17, 05:41AM. The answer to “Prove that the curl of a gradient is always zero. Check it for function (b) in Prob. 1.11.Reference Prob. 1.11.Find the gradients of the following functions:(a) f (x, y, z) = x2 + y3 + z4.(b) f (x, y, z) = x2 y3z4.(c) f (x, y, z) = ex sin(y) ln(z).” is broken down into a number of easy to follow steps, and 51 words. This full solution covers the following key subjects: prob, gradient, curl, Find, function. This expansive textbook survival guide covers 12 chapters, and 550 solutions.

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Prove that the curl of a gradient is always zero. Check it