On the basis of numerical calculations of trajectories, the peculiarities of motion of submicronsized particles in the Earth's plasmasphere are investigated. The most important result of these investigations is the found possibility of long-term residence of a microparticle in the Earth's vicinity. This effect is a result of the interaction of the electric charge, induced on a microparticle, with the magnetic field of the Earth. It is shown that the effect of microparticle capture by the Earth's magnetic field takes place in the case when the microparticles having a dimension of about 10^-2 μm and made of a material having high yield of photoemission are injected into the plasmasphere at altitudes of about several thousand kilometers and also in the case when the microparticles with a dimension of about 10^-3 μm and made of a material having low yield of photoemission are injected into the plasmasphere at altitudes of about 15000-20000 km and are moving close to the equatorial plane.