A field in which a test charge around any closed surface in static path is zero is called

A field in which the net electric flux through any closed surface is zero is characteristic of an electrostatic field in equilibrium. Specifically, this principle is encapsulated by Gauss’s Law in electrostatics, which states that the total electric flux through a closed surface is proportional to the charge enclosed by the surface. Therefore, if a test charge moves around any closed path in such a field and the net work done is zero, it implies that the electric field is conservative. However, the precise terminology you’re looking for, which describes the scenario where the net work done on a test charge over a closed path is zero, refers to a conservative electric field. Yet, your question hints at the concept encapsulated by Gauss’s Law for electrostatics, where the net electric flux out of any closed surface is proportional to the charge enclosed by the surface. If there’s no charge within the closed surface or if the positive and negative charges inside cancel out, the net electric flux would be zero, indicating an electrostatic equilibrium condition within that closed surface.