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(a) Show that Maxwell’s equations with magnetic charge

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

Solution for problem 64P 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 64P

Problem 64P

(a) Show that Maxwell’s equations with magnetic charge (Eq. 7.44) are invariant under the duality transformation

where  is an arbitrary rotation angle in “E/B-space.” Charge and current densities transform in the same way as qe and qm.

particular, that if you know the fields produced by a configuration of electric charge, you can immediately (using α = 90˚) write down the fields produced by the corresponding arrangement of magnetic charge.]

(b) Show that the force law (Prob. 7.38)

is also invariant under the duality transformation.

Problem 7.38

Assuming that “Coulomb’s law” for magnetic charges (qm) reads

work out the force law for a monopole qm moving with velocity v through electric and magnetic fields E and B.26

Step-by-Step Solution:
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Chapter 7, Problem 64P is Solved
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Textbook: Introduction to Electrodynamics
Edition: 4
Author: David J. Griffiths
ISBN: 9780321856562

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(a) Show that Maxwell’s equations with magnetic charge