In an effort to shed some light on the main features of the innermost part of the zodiacal cloud, the solar F-corona region, for which both observational and theoretical studies still give controversial results, we model the dynamics and physical evolution of dust grains at several solar radii (R⊙) from the Sun. We take into account solar gravity, direct solar radiation pressure, Poynting–Robertson force, sublimation, and the Lorentz force. The latter is computed on the base of (i) the grain surface potentials derived from elaborate model calculations and shown to vary from +3 to +12 V; (ii) a multipole radial model of the actual solar magnetic field for the period 1976–1996. The dust particles are assumed to be porous and compact spherical grains, made of two types of material: dielectric (silicate) grains and absorbing (carbon) ones.Our main results can be summarized as follows. The decrease of grains' sizes and the dynamics of particles in the orbital plane are well described by taking into account solar gravity and radiative forces together with the sublimation process, being relatively insensitive to the electromagnetic force. The silicate grains typically move inward in near-circular spirals until intensive sublimation starts and they disappear at heliocentric distances from 2 to 3R⊙. The carbon grains intensively sublimate near 4R⊙. After several radial oscillations, they are eventually ejected out as β-meteoroids, when they approach a critical radius of ≈2.4 μm (for porous grains) or ≈0.5 μm (for solid spheres), which corresponds to the radiation pressure to solar gravity ratio β equal to unity. The orientation of the orbital planes of the particles is dictated by the Lorentz force. Both porous and compact carbon grains possess high β ratios and must be larger than respectively 2.4 and 0.5 μm to reach the near-solar region. For these sizes, the Lorentz force is relatively weak, comes basically from the dipole zonal component of the field, and leads to low-amplitude oscillations of orbital inclinations and a precession of the lines of nodes. The same behavior is predicted for silicate porous (compact) grains larger than 2 μm (1 μm) and 1 μm (0.5 μm) for the periods of quiet and active Sun, respectively. From these sizes to smaller ones, the Lorentz force effectively broadens the initial distribution of inclinations of silicate grains. Submicrometer-sized particles easily get in polar and retrograde orbits well before the evaporation. On the whole, we find that the dynamics of near-solar grains depend radically on their sizes, chemical composition, and structure and, in cases of relatively small dielectric grains, may be severely correlated to the solar activity cycle.