  We have theoretically investigated the electromechanical properties of a
freely suspended carbon nanotube that is connected to a constant-current source
and subjected to an external magnetic field. We show that self-excitation of
mechanical vibrations of the nanotube can occur if the magnetic field $H$
exceeds a dissipation-dependent critical value $H_{c}$, which we find to be of
the order of 10-100 mT for realistic parameters. The instability develops into
a stationary regime characterized by time periodic oscillations in the
fundamental bending mode amplitude. We find that for nanotubes with large
quality factors and a magnetic-field strength just above $H_{c}$ the frequency
of the stationary vibrations is very close to the eigenfrequency of the
fundamental mode. We also demonstrate that the magnetic field dependence of the
time averaged voltage drop across the nanotube has a singularity at $H=H_{c}$.
We discuss the possibility of using this phenomenon for the detection of
nanotube vibrations.
