1109.2264 (Claudio Bunster et al.)

Electric charge in the field of a magnetic event in three-dimensional
spacetime    [PDF]

Claudio Bunster, Cristian Martinez

We analyze the motion of an electric charge in the field of a magnetically
charged event in three-dimensional spacetime. We start by exhibiting a first
integral of the equations of motion in terms of the three conserved components
of the spacetime angular momentum, and then proceed numerically. After crossing
the light cone of the event, an electric charge initially at rest starts
rotating and slowing down. There are two lengths appearing in the problem: (i)
the characteristic length $\frac{q g}{2 \pi m}$, where $q$ and $m$ are the
electric charge and mass of the particle, and $g$ is the magnetic charge of the
event; and (ii) the spacetime impact parameter $r_0$. For $r_0 \gg \frac{q g}{2
\pi m}$, after a time of order $r_0$, the particle makes sharply a quarter of a
turn and comes to rest at the same spatial position at which the event happened
in the past. This jump is the main signature of the presence of the magnetic
event as felt by an electric charge. A derivation of the expression for the
angular momentum that uses Noether's theorem in the magnetic representation is
given in the Appendix.

View original: http://arxiv.org/abs/1109.2264