  We examine the 1/N expansion, where N is the number of two-component Dirac
fermions, for Coulomb interactions in graphene with a gap of magnitude $\Delta
= 2 m$. We find that for $N\alpha\gg1$, where $\alpha$ is graphene's "fine
structure constant", there is a crossover as a function of distance $r$ from
the usual 3D Coulomb law, $V(r) \sim 1/r$, to a 2D Coulomb interaction, $V(r)
\sim \ln(N\alpha/mr)$, for $m^{-1} \ll r \ll m^{-1} N \alpha/6$. This effect
reflects the weak "confinement" of the electric field in the graphene plane.
The crossover also leads to unusual renormalization of the quasiparticle
velocity and gap at low momenta. We also discuss the differences between the
interaction potential in gapped graphene and usual QED for different coupling
regimes.
