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Get Full Access to Introduction To Electrodynamics - 4 Edition - Chapter 10 - Problem 14p
Get Full Access to Introduction To Electrodynamics - 4 Edition - Chapter 10 - Problem 14p

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# Suppose the current density changes slowly enough that we

ISBN: 9780321856562 45

## Solution for problem 14P Chapter 10

Introduction to Electrodynamics | 4th Edition

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Problem 14P

Problem 14P

Suppose the current density changes slowly enough that we can (to good approximation) ignore all higher derivatives in the Taylor expansion

(for clarity, I suppress the r-dependence, which is not at issue). Show that a fortuitous cancellation in Eq. 10.38 yields

That is: the Biot-Savart law holds, with J evaluated at the non-retarded time. This means that the quasistatic approximation is actually much better than we had any right to expect: the two errors involved (neglecting retardation and dropping the second term in Eq. 10.38) cancel one another, to first order.

Equation 10.38

Step-by-Step Solution:

Solution 14P

Step 1 of 3:

Here our aim is to prove that

Where (same as the notation  r)

Step 2 of 3

Step 3 of 3

##### ISBN: 9780321856562

This full solution covers the following key subjects: Approximation, higher, any, actually, better. This expansive textbook survival guide covers 12 chapters, and 550 solutions. This textbook survival guide was created for the textbook: Introduction to Electrodynamics , edition: 4. Since the solution to 14P from 10 chapter was answered, more than 281 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 14P from chapter: 10 was answered by , our top Physics solution expert on 07/18/17, 05:41AM. Introduction to Electrodynamics was written by and is associated to the ISBN: 9780321856562. The answer to “Suppose the current density changes slowly enough that we can (to good approximation) ignore all higher derivatives in the Taylor expansion (for clarity, I suppress the r-dependence, which is not at issue). Show that a fortuitous cancellation in Eq. 10.38 yields That is: the Biot-Savart law holds, with J evaluated at the non-retarded time. This means that the quasistatic approximation is actually much better than we had any right to expect: the two errors involved (neglecting retardation and dropping the second term in Eq. 10.38) cancel one another, to first order.Equation 10.38” is broken down into a number of easy to follow steps, and 92 words.

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