  The momentum-weighted sum of the electric charges of particles inside a jet,
known as jet charge, is sensitive to the electric charge of the particle
initiating the parton shower. This paper presents jet charge distributions in
$\sqrt{s_\mathrm{NN}} =$ 5.02 TeV lead-lead (PbPb) and proton-proton (pp)
collisions recorded with the CMS detector at the LHC. These data correspond to
integrated luminosities of 404 $\mu$b$^{-1}$ and 27.4 pb$^{-1}$ for PbPb and pp
collisions, respectively. Leveraging the sensitivity of the jet charge to
fundamental differences in the electric charges of quarks and gluons, the jet
charge distributions from simulated events are used as templates to extract the
quark- and gluon-like jet fractions from data. The modification of these jet
fractions is examined by comparing pp and PbPb data as a function of the
overlap of the colliding Pb nuclei (centrality). This measurement tests the
color charge dependence of jet energy loss due to interactions with the
quark-gluon plasma. No significant modification between different centrality
classes and with respect to pp results is observed in the extracted fractions
of quark- and gluon-like jet fractions.
