  Studies have shown that emission of gravitational wave drives an instability
in the $r$-modes of young rapidly rotating neutron stars carrying away most of
the angular momentum through gravitational wave emission in the first year or
so after their formation. Magnetic field plays a crucial role in the evolution
of these $r$-modes and hence the evolution of the neutron star itself. An
attempt is made here to investigate the role of magnetic field in the evolution
of $r$-mode instability and detectibility of gravitational waves emitted by a
newly born, hot and rapidly and differentially rotating neutron star. It is
found that magnetic field tend to suppress the $r$-mode amplitude. The {\it
signal-to-noise ratio} analysis shows that gravitational waves emitted from the
$r$-mode instability from neutron stars with magnetic fields upto the order of
$10^{14}$ gauss may be detectable by the Advanced LIGO at 20 Mpc.
