We examine the reduction of silver nanoparticle (AgNP) size under an external magnetic field within a classical nucleation theory framework combined with a sphere-packing description of atomic assembly. The model incorporates magnetic free-energy contributions arising from the coupling between the applied field and the magnetic susceptibility of the nucleating material, yielding a closed-form relation between nanoparticle radius and field strength. Our approach reproduces the experimentally observed decrease in the most-probable particle radius from approximately 170 nm at B=49. 27 mT when the magnetic field is oriented parallel to the stirring plane, and to 155 nm at B=180. 78 mT in the perpendicular configuration. Across the investigated field range, the theoretical predictions remain consistent with experimental measurements obtained under continuous mechanical stirring, supporting the interpretation that the observed size reduction originates from a magnetic-field-induced modification of the nucleation free-energy landscape. Within the limits of classical capillarity and spherical demagnetization, the results provide a physically transparent and computationally efficient framework for understanding magnetic-field-controlled nanoparticle size selection.
Tawalbeh et al. (Sat,) studied this question.