Work function study based on the onset method (WFS) is a surface technique used for investigation of the adsorption and deposition processes. When applied using scanning electron beam, it can be used for surface mapping of the work function with the lateral resolution presumably comparable to that of primary beam spot size. Such experimental arrangement is known as Work Function Microscopy (WFM). In the case of a non-uniform surface distribution of the work function, a contact potential is established between areas having different work function. The corresponding electrical field, known as patch field, influences work function study using the retarding field potential. Although this influence should be also present when using the onset method, this problem has not been tackled so far in these measurements. In this work we calculate the potential distribution above a single low work function patch on a high work function substrate. The potential distribution is evaluated in the presence of the external field, which is a common situation in WFS and WFM measurements. We show that WFS and WFM results may be strongly influenced by the patch field. Their interpretation depends on the external field and the size of areas (patches) having uniform local work function.