  We study motion of current-carrying string loops in the field of braneworld
spherically symmetric black holes and naked singularities. The spacetime is
described by the RN geometry with tidal charge b reflecting the non-local tidal
effects coming from the external dimension; both positive and negative values
of the spacetime parameter b are considered. We restrict attention to the
axisymmetric motion of string loops when the motion can be fully governed by an
appropriately defined effective potential related to the energy and angular
momentum of the string loops. In dependence on these two constants of the
motion, the string loops can be captured, trapped, or can escape to infinity.
In close vicinity of stable equilibrium points at the centre of trapped states
the motion is regular. We describe how it is transformed to chaotic motion with
growing energy of the string loop. In the field of naked singularities the
trapped states located off the equatorial plane of the system exist and
trajectories unable to cross the equatorial plane occur, contrary to the
trajectories in the field of black holes where crossing the equatorial plane is
always admitted. We concentrate our attention to the so called transmutation
effect when the string loops are accelerated in the deep gravitational field
near the black hole or naked singularity by transforming the oscillatory energy
to the energy of the transitional motion. We demonstrate that the influence of
the tidal charge can be substantial especially in the naked singularity
spacetimes with b>1 where the acceleration to ultrarelativistic velocities with
Lorentz factor \gamma{} ~ 100 can be reached, being more than one order higher
in comparison with those obtained in the black hole spacetimes.

General Relativity and Quantum Cosmology