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Suppose J(r) is constant in time but ?(r, t) is

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

Solution for problem 60P Chapter 7

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 60P

Problem 60P

Suppose J(r) is constant in time but ρ(r, t) is not—conditions that might prevail, for instance, during the charging of a capacitor.

(a) Show that the charge density at any particular point is a linear function of time:

where  is the time derivative of ρ at t = 0. [Hint: Use the continuity equation.]

This is not an electrostatic or magnetostatic configuration;34 nevertheless, rather surprisingly, both Coulomb’s law (Eq. 2.8) and the Biot-Savart law (Eq. 5.42) hold, as you can confirm by showing that they satisfy Maxwell’s equations. In particular:

(b) Show that

obeys Ampère’s law with Maxwell’s displacement current term.

Step-by-Step Solution:
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Chapter 7, Problem 60P is Solved
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Textbook: Introduction to Electrodynamics
Edition: 4
Author: David J. Griffiths
ISBN: 9780321856562

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Suppose J(r) is constant in time but ?(r, t) is