The following simulation shows a non-perturbed 2-D space, represented by a plane.
to run the animation during a short period of time and you will see how the plane gradually buckles due to the presence of an invisible charge that is approaching.
Continue the simulation. Try to obtain a better 3-D visualization.
The previous simulation has been performed (with a little bit of trickery) as follows: a uniform vertical field has been established, and an invisible charge has been placed far away from the plane. When "animation" is started, the charge approaches the plane and the plotted equipotential surface is being modified. The presentation has been achieved in the following way: