Sandstorms are frequently accompanied by intense electric fields and lightning. In a very narrow region close to the ground, sand particles undergo a charge exchange during which larger-sized sand grains become positively charged and smaller-sized sand grains become negatively charged and then all particles become suspended by the turbulent fluid motion. Although the association of intense electric fields with sandstorms has long been observed, the mechanism that causes these intense electric fields has not yet been described. Here, we hypothesize that differently sized sand particles are differentially transported by turbulence in the flow, resulting in a large-scale charge separation and a consequential large-scale electric field. To confirm our hypothesis, we combined a large-eddy simulation framework comprising a turbulent atmospheric boundary layer and movement of sand particles with an electrostatic Gauss law to investigate the physics of the electric fields in sandstorms. We varied the strength of the sandstorm from weak to strong as parametrized by the number density of the entrained sand particles. Our simulations reproduced observational measurements of both mean and root mean squared fluctuation values of the electric field. Our results allowed us to propose a law in which the electric field scales to two-thirds of the power of the concentration of the sand particles in weak-to-medium strength sandstorms. The underlying approach to simulate the solid particle-laden flow is Eulerian-Eulerian in which the particles are characterized by statistical descriptors. To explore the essential physics of the electric field generation in a sandstorm, we model the high-Reynolds-number atmospheric boundary-layer (ABL) using two different canonical turbulent flows: one model is that of a turbulent boundary-layer (TBL), and the second one is that of a turbulent half-channel flow. For the particle phase, the direct quadrature method of moments (DQMOM) is chosen in which the abscissas and weights of the quadrature method are tracked directly. The utilization of this framework is proposed to examine the transport of sand in sandstorms. Furthermore, the physical mechanisms necessary for production and sustenance of large-scale electric fields in sandstorms is investigated.