We investigate the anomalous flavour changing neutral current (FCNC) interactions of top quark through the process $e^{-}pto e^{-}W^{pm}q+X$. We calculate the signal and background cross sections in electron proton collisions at Large Hadron electron Collider (LHeC) with a 7 TeV proton beam from the LHC and a new 60 GeV electron beam from energy recovery linac (ERL). We study the relevant background processes including one electron and three jets in the final state. The distributions of the invariant mass of two jets and an additional jet tagged as $b$-jet are used to account signal and background events after the analysis cuts. We find upper bounds on anomalous FCNC couplings $lambda$ of the order of $10^{-2}$ at LHeC for a luminosity projection of $100$ fb$^{-1}$ together with the fast simulation of detector effects. As a matter of interest, we analyze the sensitivity to the couplings $(lambda_{u},lambda_{c})$ and find an enhanced sensitivity to $lambda_{c}$ at the LHeC when compared to the results from the HERA.
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