We present a D-dimensional charged Anti-de-Sitter black hole solutions in
f(T) gravity, where f(T)=T+βT2 and D≥4. These solutions are
characterized by flat or cylindrical horizons. The interesting feature of these
solutions is the existence of inseparable electric monopole and quadrupole
terms in the potential which share related momenta, in contrast with most of
the known charged black hole solutions in General Relativity and its
extensions. Furthermore, these solutions have curvature singularities which are
milder than those of the known charged black hole solutions in General
Relativity and Teleparallel Gravity. This feature can be shown by calculating
some invariants of curvature and torsion tensors. Furthermore, we calculate the
total energy of these black holes using the energy-momentum tensor. Finally, we
show that these charged black hole solutions violate the first law of
thermodynamics in agreement with previous results.Comment: 11 Pages, will appear in JHE