  The equilibrium configuration of white dwarfs composed of a charged perfect
fluid are investigated in the context of the $f(R,\mathcal{T})$ gravity, for
which $R$ and $\mathcal{T}$ stand for the Ricci scalar and the trace of the
energy-momentum tensor, respectively. By considering the functional form $f(R,
\mathcal{T})=R+2\chi \mathcal{T}$, where $\chi$ is the matter-geometry coupling
constant, and for a Gaussian ansatz for the electric distribution, some
physical properties of charged white dwarfs were derived, namely: mass, radius,
charge, electric field, effective pressure and energy density; their dependence
on the parameter $\chi$ was also derived. In particular, the $\chi$ value
important for the equilibrium configurations of charged white dwarfs has the
same scale of $10^{-4}$ of that for non-charged stars and the order of the
charge was $10^{20}$C, which is scales with the value of one solar mass, i.e.,
$\sqrt{G}M_\odot\sim 10^{20}$C. We have also shown that charged white dwarf
stars in the context of the $f(R,\mathcal{T})$ have surface electric fields
generally below the Schwinger limit of $1.3\times 10^{18}$V/m. In particular, a
striking feature of the coupling between the effects of charge and
$f(R,\mathcal{T})$ gravity theory is that the modifications in the background
gravity increase the stellar radius, which in turn diminishes the surface
electric field, thus enhancing stellar stability of charged stars. Most
importantly, our study reveals that the present $f(R,T)$ gravity model can
suitably explain the super-Chandrasekhar limiting mass white dwarfs, which are
supposed to be the reason behind the over-luminous SNeIa and remain mostly
unexplained in the background of general relativity (GR).
