New sources of CP violation beyond the Standard Model of particle physics could be revealed in the laboratory by measuring a non-zero electric dipole moment (EDM) of a spin 1/2 particle such as the neutron. Despite the great sensitivity attained after 60 years of developments, the result of the experiments is still compatible with zero. Still, new experiments have a high discovery potential since they probe new physics at the multi-TeV scale, beyond the reach of direct searches at colliders. Progress in precision on the neutron EDM is limited by a systematic effect arising from the relativistic motional field $vec{E} times vec{v} / c^2$ experienced by the particles moving in the measurement chamber in combination with the residual magnetic gradients. This effect would normally forbid a significant increase of the size of the chamber, sadly hindering the increase of neutron statistics. We propose a new measurement concept to evade this limitation in a room-temperature experiment employing a mercury co-magnetometer. It consists ajusting the static magnetic field $B_0$ to a `magic value which cancels the false EDM of the mercury. The magic setting is $7.2,muT$ for a big cylindrical double-chamber of diameter $100$~cm.
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