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A time-dependent point charge q(t) at the origin, is fed

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

Solution for problem 7P Chapter 10

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 7P

A time-dependent point charge q(t) at the origin,  is fed by a current

(a) Check that charge is conserved, by confirming that the continuity equation is obeyed.

(b) Find the scalar and vector potentials in the Coulomb gauge. If you get stuck, try working on (c) first.

(c) Find the fields, and check that they satisfy all of Maxwell’s equations.3

Step-by-Step Solution:

Solution 7P

Step 1 of 3:

Consider a time dependent point charge  at the origin,  is fed by a current .

  1. We need to check that, the charge is conserved by confirming that the continuity equation is obeyed.

Given

                                

We know that,

                                

We have,

                                

So,

                                

                                

We have                 

So,

                                

Continuity equation verified, so the charge is conserved.


Step 2 of 3

Chapter 10, Problem 7P is Solved
Step 3 of 3

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

The full step-by-step solution to problem: 7P from chapter: 10 was answered by , our top Physics solution expert on 07/18/17, 05:41AM. Since the solution to 7P from 10 chapter was answered, more than 1001 students have viewed the full step-by-step answer. The answer to “A time-dependent point charge q(t) at the origin, is fed by a current (a) Check that charge is conserved, by confirming that the continuity equation is obeyed.(b) Find the scalar and vector potentials in the Coulomb gauge. If you get stuck, try working on (c) first.(c) Find the fields, and check that they satisfy all of Maxwell’s equations.3” is broken down into a number of easy to follow steps, and 58 words. This textbook survival guide was created for the textbook: Introduction to Electrodynamics , edition: 4. This full solution covers the following key subjects: Charge, check, Find, conserved, continuity. This expansive textbook survival guide covers 12 chapters, and 550 solutions. Introduction to Electrodynamics was written by and is associated to the ISBN: 9780321856562.

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A time-dependent point charge q(t) at the origin, is fed