  We study the static equilibrium of a charged massive particle around a
charged black hole, balanced by the Lorentz force. For a given black hole, the
equilibrium surface is determined by the charge/mass ratio of the particle. By
investigating a large class of charged black holes, we find that the equilibria
can be stable, marginal or unstable. We focus on the unstable equilibria which
signal chaotic motions and we obtain the corresponding Lyapunov exponents
$\lambda$. We find that although $\lambda$ approaches universally the horizon
surface gravity $\kappa$ when the equilibria are close to the horizon, the
proposed chaotic motion bound $\lambda<\kappa$ is satisfied only by some
specific black holes including the RN and RN-AdS black holes. The bound can be
violated by a large number of black holes including the RN-dS black holes or
black holes in Einstein-Maxwell-Dilaton, Einstein-Born-Infeld and
Einstein-Gauss-Bonnet-Maxwell gravities. We find that unstable equilibria can
even exist in extremal black holes, implying that the ratio $\lambda/\kappa$
can be arbitrarily large for sufficiently small $\kappa$. Our investigation
does suggest a universal bound for sufficiently large $\kappa$, namely
$\lambda/\kappa <{\cal C}$ for some order-one constant ${\cal C}$.
