Classical Electrodynamics · Problem 6.17

Plane Electromagnetic Waves and Wave Propagation — John David Jackson

Physics — E&M · dyon-lorentz-force-dirac-quantization-generalized

Problem

(a) For a particle possessing both electric and magnetic charges, show that the generalization of the Lorentz force in vacuum is

\mathbf{F} = q_e \mathbf{E} + q_m \mathbf{B}/\mu_0 + q_e \mathbf{v} \times \mathbf{B} - q_m \mathbf{v} \times \epsilon_0 \mathbf{E}

(b) Show that this expression for the force is invariant under a duality transformation of both fields and charges, (6.151) and (6.152). (c) Show that the Dirac quantization condition, (6.153), is generalized for two particles possessing electric and magnetic charges

e_1, g_1

and

e_2, g_2

, respectively, to

\frac{e_1 g_2 - e_2 g_1}{\hbar} = 2\pi n

and that the relation is invariant under a duality transformation of the charges.

Related theory

Lorentz Force

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