So if I have two parallel metal sheets separated by 0.1 meters with air as a dielectric with a breakdown strength of 3MV/m and I'm applying a voltage pulse that goes from 0 to 100kV in few microseconds (so we shouldn't have an arc between the two plates as the electric field is below the breakdown of air) Now assume that one of the plates got a rough surface hence a lot of sharp spikes, so there is an amplification of the electric field by a factor of 10 or even 100x that causes a breakdown to occur between the two plates through the air. How would you find how much force was exerted on the 2nd plate due to the huge electric field? Basically trying to find out if the surface of the 2nd plate would bend.
BTW I don't care about exact numbers, just looking for the general way to think about this problem. I know for a parallel plate capacitor with uniform electric field the force is F = (Permativity * Voltage ^2 * surface area)/(2*distance^2) But this isn't uniform electric field as the spikes on the surface will have much higher fields.
Also is it fair to say that when the electric field got amplified by 10x, the potential difference between this spike and the other ground plane (2nd plate) was also amplified by 10x but it wasn't a sustainable potential difference as the arc/spark connected the two metals together and got rid of this potential difference?