In fact, a change in the electric field will propagate from the electrode at the speed of light. (More precisely, at the speed of propagation of radio waves. Material constants have different values in the radio range than at optical frequencies.) The speed of light is 300 mm/ps, and your dimensions are on the order of µm. Therefore the transit time for propagating the change in the electric field is much shorter than ps. I’m sure the time constant of your electrodes will be longer than that!