  The foundational theory for dusty plasmas is the dust charging theory that
provides the dust potential and charge arising from the dust interaction with a
plasma. The most widely used dust charging theory for negatively charged dust
particles is the so-called orbital motion limited (OML) theory, which predicts
the dust potential and heat collection accurately for a variety of
applications, but was previously found to be incapable of evaluating the dust
charge and plasma response in any situation. Here we report a revised OML
formulation that is able to predict the plasma response and hence the dust
charge. Numerical solutions of the new OML model show that the widely-used
Whipple approximation of dust charge-potential relationship agrees with OML
theory in the limit of small dust radius compared with plasma Debye length, but
incurs large (order-unity) deviation from the OML prediction when the dust size
becomes comparable with or larger than plasma Debye length. This latter case is
expected for the important application of dust particles in a tokamak plasma.
