It is well known that one can create a magnetic field by passing a DC or AC electric current through a coil of conductor (i.e., a wire); a phenomenon described by the Maxwell-Faraday’s law of electromagnetic induction. NMR or ESR (nuclear magnetic resonance or electron spin resonance) spectroscopies involve the interaction of a spin (nuclear or electron, respectively) with a magnetic field. Mathematically, these phenomena can be understood as the curl of the electric field (i.e., the current or spin) producing a (time varying) magnetic field or vise versa. Thus, one should also be able to induce a magnetic response in nano- and meso-scale materials by exploiting Maxwell-Faraday’s law of induction through the design of the structure, by employing an electric field with instantaneous curl or do both to produce an instantaneous circulating (or displacement) current. Here we employ cylindrical vector beams with azimuthal polarization to create an angular (cylindrical) electric field, and selectively induce a magnetic response in metal nanoparticle-based nanomaterials at optical frequencies. This time-varying magnetic field at optical frequencies is induced in systems that do not possess spin or orbital angular momentum. Moreover, with the vector beam spectroscopy we also selectively drive electric dipole modes by excitation with a radially polarized light, and show that the strength of the electric and magnetic modes can be equal in magnitude in individual metal nano-structures. This work opens new opportunities for selective spectroscopic investigation of “dark modes” and Fano resonances in nanomaterials, metamaterials and control of nanomaterial excitations and dynamics.