  The measurement of the top-quark anomalous electromagnetic couplings is one
of the most important goals of the top-quark physics program in the present and
future collider experiments. This would provide direct information on the
non-standard interactions of the top-quark. We study a top-quark pair
production scenario at the Future Circular Collider Hadron-Electron (FCC-he)
through $e^-p \to e^-\gamma^*\gamma^*p \to e^-t\bar t p$ collisions, which will
provide information about sensitivities on anomalous $\hat a_V$ and $\hat a_A$
couplings at $95\%\hspace{0.8mm}C.L.$, and the possibility of probing new
physics. Energy of the $e^-$ beams is taken to be $E_e=250\hspace{0.8mm}GeV$
and $500\hspace{0.8mm}GeV$ and the energy of the $p$ beams is taken to be
$E_p=50\hspace{0.8mm}TeV$, with these energies the FCC-he may sensitivity
estimates on top-quark electromagnetic dipole moments $\hat a_V$ and $\hat a_A$
of the order ${\cal O}(10^{-2}-10^{-1})$.
