Dielectric nanoparticles with moderately high refractive index and very low absorption (like Si and Ge in the visible-near-infrared (VIS-NIR) range) show a magnetodielectric behavior that produces interesting far-field coherent effects, like directionality phenomena or field enhancement in the proximity of the particle surface. As in the case of metals, ensembles of two or more dielectric particles can constitute basic elements for developing new spectroscopic tools based on surface field enhancement effects. Here we explore the electromagnetic behavior of the basic unit constituted by a dimer of dielectric nanoparticles made of moderately low-loss high refractive index material. The interactions responsible for the spectral features of the scattered radiation and field enhancement of the dimer are identified and studied through an analytical dipole-dipole model. The fluorescence of a single emitter (either electric or magnetic dipole) located in the dimer gap is also explored by calculating the quantum efficiencies and the quenching/enhancement of the radiation rates. Along this analysis, a comparison with metallic dimers is carried out. This study opens new possibilities to perform field-enhanced spectroscopy and sensing with nanostructures made of suitable dielectric materials.