  Determining the equilibrium charge of conducting spheres in plasmas is
important for interpreting Langmuir probe measurements, plasma surface
interactions and dust particle behaviour. The Monte Carlo code Dust in
Magnetised Plasmas (DiMPl) has been developed for the purpose of determining
the forces and charging behaviour of conducting spheroids under a variety of
conditions and benchmarked against previous numerical results. The floating
potentials of spheres in isothermal, collisionless, hydrogen plasmas as a
function of magnetic field strength and size relative to Debye length are
studied using DiMPl and compared with new results from the N-body tree code
(pot) and recent particle in cell measurements. The results of all three
simulations are similar, identifying a small range at modest ion magnetisation
parameters over which the electron current is reduced relative to the ion
current. The potential as a function of magnetic field strength is found to be
relatively insensitive to dust size for dust smaller than the Debye length. The
potential of large dust is found to depend less strongly on flow speed for
modest magnetic field strengths and to decrease with increasing flow speed in
the presence of strong magnetic fields for smaller dust. A semi-empirical model
for the potential of small dust in a collisionless plasma as a function of
magnetic field strength is developed which reproduces the expected currents and
potentials in the high and low magnetic field limit.
