  The spectral stability of liquid metal differentially rotating in transverse
magnetic field is studied numerically by solving the eigenvalue problem with
rigid-wall boundary conditions. The equilibrium velocity profile used in
calculations corresponds to the electrically driven flow in circular channel
with the rotation law \Omega(r)~1/r^2. This type of flow profile is planned to
be used in new experimental device to test the magnetorotational instability
(MRI) in laboratory. Our analysis includes calculations of the eigen-frequency
spectra for both axisymmetric and non-axisymmetric modes. It is found that for
chosen device parameters the flow is always spectrally unstable due to MRI with
the fastest growth rate corresponding to the axisymmetric mode.
