  We investigate the potential for discovering new physics through the
low-energy scattering processes $e^-p\to e^-(\mu^-)\Lambda_c$, which could be
accessible in the forthcoming $ep$ scattering experiments once adapted to our
proposed setups. In the framework of a general low-energy effective Lagrangian,
we demonstrate that, compared with the conventional flavor-changing
neutral-current weak decays of charmed hadrons and the dilepton productions at
high-energy colliders, the low-energy scattering processes can provide more
competitive potentials for hunting the underlying new physics. In some specific
leptoquark models, we also show that promising event rates can be expected for
both the scattering processes, and point out a possible way to distinguish the
experimental signals due to the scalar leptoquarks from those of the vector
ones.
