  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 $e^-p
\to e^-\gamma p \to \bar t \nu_e b p$. 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 $\delta_{sys}=0\%, 3\%, 5\%$ 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.
