  Aims. The surfaces of the Trojan asteroids are steadily bombarded by
interplanetary micrometeoroids, which releases ejecta of small dust particles.
These particles form the faint dust arcs that are associated with asteroid
clouds. Here we analyze the particle dynamics and structure of the arc in the
region of the $L_4$ Trojan asteroids.
  Methods. We calculate the total cross section of the $L_4$ Trojan asteroids
and the production rate of dust particles. The motion of the particles is
perturbed by a variety of forces. We simulate the dynamical evolution of the
dust particles, and explore the overall features of the Trojan dust arc.
  Results. The simulations show that the arc is mainly composed of grains in
the size range 4-10 microns. Compared to the $L_4$ Trojan asteroids, the dust
arc is distributed more widely in the azimuthal direction, extending to a range
of [30,120] degrees relative to Jupiter. The peak number density does not
develop at $L_4$. There exist two peaks that are azimuthally displaced from
$L_4$.
