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 $e^-p \to e^-��^*��^*p \to e^-t\bar t p$ 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 ${\cal O}(10^{-2}-10^{-1})$.

27 Pages, 12 Figures and 7 Tables, version to be published on EPJP. arXiv admin note: text overlap with arXiv:1702.03708