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From the elastic point of view, the twist-bend nematic phase, (NTB), has a ground state characterised by a spontaneous bend with a precession of the directornalong the direction of an axist. The tilt angle θ formed between the directornand the axistgives rise to a heliconical structure with a nanometric helical pitchp. Using an elastic continuum theory recently proposed as an extension of the Frank energy for these materials, we investigate the influence of an external magnetic field on the pitch of the NTBphase. For a material with positive magnetic susceptibility anisotropy, when the magnetic fieldHis perpendicular tot, it is shown that the pitch of the nematic directornprecession increases withH, and at a critical value ofit becomes infinite as in a cholesteric liquid crystal, that is, one gets a uniform orientation ofn. Our results include the behaviour of a cholesteric under field as a limiting case, and are obtained in the simple case where θ is assumed as uniform throughout the sample. [ABSTRACT FROM AUTHOR]