  Intense attosecond magnetic field pulses are predicted to be produced by
intense few cycle circularly polarized UV pulses. Numerical solutions of the
time dependent Schr\"{o}dinger equation for H$_2^+$ are used to study the
dynamical process. Spiralling attosecond circular electron wave packets are
created with nanometer molecular dimensions, thus generating magnetic fields of
several tens of Teslas ($10^5$ Gauss). Simulations show that the induced
magnetic field is critically dependent on the pulse wavelength $\lambda$ and
pulse duration $n\tau$ ($n$ number of cycle) as predicted by a classical model.
For ultrashort few cycle circularly polarized attosecond pulses, molecular
orientation influences the generation of the induced magnetic fields as a
result of preferential ionization perpendicular to the molecular axis.
