  Theory and simulations suggest that magnetic fields from radio jets and lobes
powered by their central super massive black holes can be an important source
of magnetic fields in the galaxy clusters. This is paper II in a series of
studies where we present self-consistent high-resolution adaptive mesh
refinement cosmological magnetohydrodynamic (MHD) simulations that
simultaneously follow the formation of a galaxy cluster and evolution of
magnetic fields ejected by an active galactic nucleus (AGN). We studied 12
different galaxy clusters with virial masses ranging from 1 $\times$ 10$^{14}$
to 2 $\times$ 10$^{15}$ M$_{\odot}$. In this work we examine the effects of the
mass and merger history on the final magnetic properties. We find that the
evolution of magnetic fields is qualitatively similar to those of previous
studies. In most clusters, the injected magnetic fields can be transported
throughout the cluster and be further amplified by the intra-cluster medium
(ICM) turbulence during the cluster formation process with hierarchical
mergers, while the amplification history and the magnetic field distribution
depend on the cluster formation and magnetism history. This can be very
different for different clusters. The total magnetic energies in these clusters
are between 4 $\times$ 10$^{57}$ and $10^{61}$ erg, which is mainly decided by
the cluster mass, scaling approximately with the square of the total mass.
Dynamically older relaxed clusters usually have more magnetic fields in their
ICM. The dynamically very young clusters may be magnetized weakly since there
is not enough time for magnetic fields to be amplified.
