  The top quark flavor changing neutral current (FCNC) processes are extremely
suppressed within the Standard Model (SM) of particle physics. However, they
could be enhanced in a new physics model Beyond the Standard Model (BSM). The
top quark FCNC interactions would be a good test of new physics at present and
future colliders. Within the framework of the BSM models, these interactions
can be described by an effective Lagrangian. In this work, we study tqgamma and
tqZ effective FCNC interaction vertices through the process e-p->e-Wq+X at
future electron proton colliders, projected as Large Hadron electron Collider
(LHeC) and Future Circular Collider-hadron electron (FCC-he). The cross
sections for the signal have been calculated for different values of parameters
lambda_q for tqgamma vertices and kappa_q for $tqZ$ vertices. Taking into
account the relevant background we estimate the attainable range of signal
parameters as a function of the integrated luminosity and present contour plots
of couplings for different significance levels including detector simulation.
