We have developed a method of calculation of the dielectrophoretic force on a nanoparticle in a fluid environment where variations in the electric field and electric field gradients are on the same nanoscale as the particle. The Boundary Element Dielectrophoretic Force (BEDF) method involves constructing a solvent-accessible or molecular surface surrounding the particle, calculating the normal component of the electric field at the surface boundary elements, and then solving a system of linear equations for the induced surface polarization charge on each element. Different surface elements of the molecule may experience quite different polarizing electric fields, unlike the situation in the point dipole approximation. A single 100-Angstrom-radius ring test configuration is employed to facilitate comparison with the well-known point dipole approximation (PDA). We find remarkable agreement between the forces calculated by the BEDF and PDA methods for a 1 Angstrom polarizable sphere. However, for larger particles, the differences between the methods become qualitative as well as quantitative; the character of the force changes from attractive at the origin of the ring for a 50-Angstrom sphere, to repulsive for a 75-Angstrom sphere. Equally dramatic differences are found in a more complex electrical environment involving two sets of 10 rings.