  As a continuation of our recent work on the electromagnetic properties of the
doubly charmed $\Xi_{cc}$ baryon, we compute the charge radii and the magnetic
moments of the singly charmed $\Sigma_c$, $\Omega_c$ and the doubly charmed
$\Omega_{cc}$ baryons in 2+1 flavor Lattice QCD. In general, the charmed
baryons are found to be compact as compared to the proton. The charm quark acts
to decrease the size of the baryons to smaller values. We discuss the mechanism
behind the dependence of the charge radii on the light valence- and sea-quark
masses. The magnetic moments are found to be almost stable with respect to
changing quark mass. We investigate the individual quark sector contributions
to the charge radii and the magnetic moments. The magnetic moments of the
singly charmed baryons are found to be dominantly determined by the light quark
and the role of the charm quark is significantly enhanced for the doubly
charmed baryons.
