Nowadays there is an increasing demand for the cost-effective monitoring of potential threats to the integrity of high-voltage networks and electric power infrastructures. Optical fiber sensors are a particularly interesting solution for applications in these environments, due to their low cost and positive intrinsic features, including small size and weight, dielectric properties, and invulnerability to electromagnetic interference (EMI). However, due precisely to their intrinsic EMI-immune nature, the development of a distributed optical fiber sensing solution for the detection of partial discharges and external electrical fields is in principle very challenging. Here, we propose a method to exploit the third-order and second-order nonlinear effects in silica fibers, as a means to achieve highly sensitive distributed measurements of external electrical fields in real time. By monitoring the electric-field-induced variations in the refractive index using a highly sensitive Rayleigh-based CP-φOTDR scheme, we demonstrate the distributed detection of Kerr and Pockels electro-optic effects, and how those can assign a new sensing dimension to optical fibers, transducing external electric fields into visible minute disturbances in the guided light. The proposed sensing configuration, electro-optical time domain reflectometry, is validated both theoretically and experimentally, showing experimental second-order and third-order nonlinear coefficients, respectively, of χ⁽²⁾ ~ 0.27 × 10^-12 m/V and χ⁽³⁾ ~ 2.5 × 10^-22 m²/V² for silica fibers.