Solution Found!
Use the duality transformation (Prob. 7.64) to construct
Chapter 11, Problem 29P(choose chapter or problem)
Problem 29P
Use the duality transformation (Prob. 7.64) to construct the electric and magnetic fields of a magnetic monopole qm in arbitrary motion, and find the “Larmor formula” for the power radiated
Reference prob 7.64
iv class="question">
(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.
Questions & Answers
QUESTION:
Problem 29P
Use the duality transformation (Prob. 7.64) to construct the electric and magnetic fields of a magnetic monopole qm in arbitrary motion, and find the “Larmor formula” for the power radiated
Reference prob 7.64
iv class="question">
(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.
ANSWER:
Solution
Step 1 of 3
In this problem, we have to show that Maxwell’s equations with magnetic charge are invariant under the duality transformation.