  We suggest that high-order g modes can be used as a probe of the internal
magnetic field of SPB (slowly pulsating B) stars. The idea is based on earlier
work by the authors which analytically investigated the effect of a vertical
magnetic field on p and g modes in a plane-parallel isothermal stratified
atmosphere. It was found that even a weak field can significantly shift the
g-mode frequencies -- the effect increases with mode order. In the present
study we adopt the classical perturbative approach to estimate the internal
field of a 4 solar mass SPB star by looking at its effect on a low-degree
($l=1$) and high-order ($n=20$) g mode with a period of about 1.5 d. We find
that a polar field strength of about 110 kG on the edge of the convective core
is required to produce a frequency shift of 1%. Frequency splittings of that
order have been observed in several SPB variables, in some cases clearly too
small to be ascribed to rotation. We suggest that they may be due to a poloidal
field with a strength of order 100 kG, buried in the deep interior of the star.
