  The electromagnetic form factors of the proton and the neutron are computed
within lattice QCD using simulations with quarks masses fixed to their physical
values. Both connected and disconnected contributions are computed. We analyze
two new ensembles of $N_f = 2$ and $N_f = 2 + 1 + 1$ twisted mass
clover-improved fermions and determine the proton and neutron form factors, the
electric and magnetic radii, and the magnetic moments. We use several values of
the sink-source time separation in the range of 1.0 fm to 1.6 fm to ensure
ground state identification. Disconnected contributions are calculated to an
unprecedented accuracy at the physical point. Although they constitute a small
correction, they are non-negligible and contribute up to 15% for the case of
the neutron electric charge radius.
