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Get Full Access to Introduction To Electrodynamics - 4 Edition - Chapter 1 - Problem 32p
Get Full Access to Introduction To Electrodynamics - 4 Edition - Chapter 1 - Problem 32p

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# Check the fundamental theorem for gradients, using T = x2

ISBN: 9780321856562 45

## Solution for problem 32P Chapter 1

Introduction to Electrodynamics | 4th Edition

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Problem 32P

Problem 32P

Check the fundamental theorem for gradients, using T = x2 + 4xy + 2yz3, the points a = (0, 0, 0), b = (1, 1, 1), and the three paths in Fig. 1.28:

(a) (0, 0, 0) (1, 0, 0) (1, 1, 0) (1, 1, 1);

(b) (0, 0, 0) (0, 0, 1) (0, 1, 1) (1, 1, 1);

(c) the parabolic path z = x2; y = x.

Fig. 1.28

Step-by-Step Solution:

Solution 32P

Step 1 of 6:

In this question, we need to check the fundamental theorems for gradients

Given

The paths given

(c) the parabolic path

Step 2 of 6

Step 3 of 6

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