  We study the role of time dependent magnetic ellipticities ($\epsilon_{B}$)
on the calculation of the braking index of pulsars. Moreover, we study the
consequences of such a $\epsilon_{B}$ on the amplitude of gravitational waves
(GWs) generated by pulsars with measured braking indices. We show that, since
the ellipticity generated by the magnetic dipole is extremely small, the
corresponding amplitude of GWs is much smaller than the amplitude obtained via
the spindown limit.
