High-permittivity dielectric particles with resonant magnetic properties are being explored as constitutive elements of new metamaterials and devices. Magnetic properties of low-loss dielectric nanoparticles in the visible or infrared are not expected due to intrinsic low refractive index of optical media in these regimes. Here we analyze the dipolar electric and magnetic response of lossless dielectric spheres made of moderate permittivity materials. For low material refractive index (<∼3) there are no sharp resonances due to strong overlapping between different multipole contributions. However, we find that Silicon particles with index of refraction∼3.5 and radius∼200 nm present strong electric and magnetic dipolar resonances in telecom and near-infrared frequencies, (i.e. at wavelengths≈1.2-2 mm) without spectral overlap with quadrupolar and higher order resonances. The light scattered by these Si particles can then be perfectly described by dipolar electric and magnetic fields.