  In this paper, we investigate the bound-state solutions of the noncommutative
Dirac oscillator with a permanent electric dipole moment in the presence of an
electromagnetic field in (2+1)-dimensions. We consider a radial magnetic field
generated by anti-Helmholtz coils, and the uniform electric field of the Stark
effect. Next, we determine the bound-state solutions of the system, given by
the two-component Dirac spinor and the relativistic energy spectrum. We note
that this spinor is written in terms of the generalized Laguerre polynomials,
and this spectrum is a linear function on the potential energy $U$, and depends
explicitly on the quantum numbers $n$ and $m$, spin parameter $s$, and of four
angular frequencies: $\omega$, $\tilde{\omega}$, $\omega_\theta$, and
$\omega_\eta$, where $\omega$ is the frequency of the oscillator,
$\tilde{\omega}$ is a type of ``cyclotron frequency'', and $\omega_\theta$ and
$\omega_\eta$ are the noncommutative frequencies of position and momentum.
Besides, we discussed some interesting features of such a spectrum, for
example, its degeneracy, and then we graphically analyze the behavior of the
spectrum as a function of the four frequencies for three different values of
$n$, with and without the influence of $U$. Finally, we also analyze in detail
the nonrelativistic limit of our results, and comparing our problem with other
works, where we verified that our results generalize several particular cases
of the literature.
