Modeling electric fields and forces around a channel in a planar membrane is still an open problem. Until now, most of the existing theories have oversimplified the electric field distribution by placing the electrode directly at the entry of the channel. However, in any relevant experimental setup the electrodes are placed far away in the electrolyte solution. We demonstrate that long-range deformation of the electric field distribution appears around the membrane, spanning on distances of the order of the distance between the membrane and the electrode. The forces acting due to this distribution are in most of the cases negligible. They can be important for channels with radii of the order of the thickness of the layer of structured water at the oil-water interface.