The magnetorotational instability (MRI), also known as the Balbus -- Hawley
instability, is thought to have an important role on the initiation of
turbulence and angular momentum transport in accretion discs. In this work, we
investigate the effect of the magnetic field gradient in the azimuthal
direction on MRI. We solve the magnetohydrodynamic equations by including the
azimuthal component of the field gradient. We find the dispersion relation and
calculate the growth rates of the instability numerically. The inclusion of the
azimuthal magnetic field gradient produces a new unstable region on wavenumber
space. It also modifies the growth rate and the wavelength range of the
unstable mode: the higher the magnitude of the field gradient, the greater the
growth rate and the wider the unstable wavenumber range. Such a gradient in the
magnetic field may be important in T Tauri discs where the stellar magnetic
field has an axis which is misaligned with respect to the rotation axis of the
disc.Comment: 8 pages, 3 figures, accepted for publication in A
