We have studied a system of discotic particles with a central transverse dipole using Monte Carlo (MC) computer simulations at constant pressure. We have investigated several temperatures corresponding to nematic and columnar liquid crystal phases and determined the molecular and dipolar organizations. Low temperature columnar phases are characterized by local biaxial ordering of dipoles, even if the system is on the whole uniaxial. However, simulations in the presence of a transverse Ðeld for di †erent Ðeld and dipole strengths show that the system has a large susceptibility and easily becomes biaxial, making it potentially interesting for switching applications. An explicit formulation for the susceptibility in terms of biaxial invariants is derived.