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.
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