A system of earthing conductors in homogeneous soil is observed, consisting of a grid earthing conductor of the plant and a ring earthing conductor of the fence that is not connected to this grid. The calculation of the potential on the surface along different directions is made using a program based on the mean potential method. It is shown how this potential changes due to the presence of the ring earthing conductor of the fence. The corresponding patterns of potential changes and critical points along the fence are observed.