Simulation of the atmospheric electric field and current structure for sensors with different geometry in relation to the electric current measured in the external circuit

Electric field measurements have many scientific applications. Their results can be used in atmospheric electricity, optimisation of electric safety, e.g. lightning protection and meteorology. However, a measurement should be performed equally reliably to draw reliable conclusions. In theory and practice, you can find various measurement methods, some used for many years and which can be verified in terms of their accuracy using the possibility of computer simulations. This work contains a field analysis of examples of electric field sensors, based on which a discussion was held and practical conclusions were drawn. Described measurement methodology is often used for measurements of lightning electric field distribution. The article concerns the theory of sensors for measuring electric field and current based on numerical simulations. It can be used both in the problems of the physics of atmospheric lightning discharges and fair-weather electricity. Electric field E and $\mathbf{\Delta} \mathbf{E}$ measurements are widely described in the literature and have large technical applications. Measurements of the Maxwell current density and its components for thunderstorm electricity and fair weather conditions are associated with many interpretations and technical difficulties. It may touch cases like currents under a thundercloud approaching or currents from distant discharges. For example, Krider and Musser [1] determined the Maxwell current in a situation where $\mathbf{Ez}(\mathbf{t}) =\mathbf{0}$ (conduction current is that it always vanishes when E is zero). Current measurement methods based directly on Gauss or Ampere-Maxwell equations and selecting appropriate sensor surfaces to carry out the integration operation on these surfaces or the path that bounds that surface may prove difficult or impossible. It needs to choose a unique Gaussian surface to calculate the electric field and a particular Amperian loop to determine the magnetic field and current density.