In this paper, we study the production of a top-quark in association with a bottom-quark and a electron-neutrino at the Future Circular Collider Hadron Electron (FCC-he) to probe the sensitivity on its magnetic moment $(\hat a_V)$ and its electromagnetic dipole moment $(\hat a_A)$ through the process $e^-p \to e^-��p \to \bar t ��_e b p$. Assuming a large amount of collisions, as well as of data with cleaner environments, the FCC-he is an excellent option to study new physics, such as the $\hat a_V$ and $\hat a_A$. For our sensitivity study on $\hat a_V$ and $\hat a_A$, we consider center-of-mass energies $\sqrt{s}= 7.07, 10\hspace{0.8mm}TeV$ and luminosities ${\cal L}=50, 100, 300, 500, 1000\hspace{0.8mm}fb^{-1}$. In addition, we apply systematic uncertainties $��_{sys}=0\%, 3\%, 5\%$ and we consider unpolarized and polarized electron beam. Our results show that the FCC-he is a very good perspective to probe the $\hat a_V$ and $\hat a_A$ at high-energy and high-luminosity frontier.

19 pages, 14 Figures, 6 Tables; v2: version published in NPB. arXiv admin note: text overlap with arXiv:1811.10462