What if gap is irregular in capacitor

[Gunmo]

I don't have clear concept on voltage. I am a Mechanical guy.
If the gap is irregular in large capacitor, how voltage is derived in theory. Using software I can divide the surface into many pieces and calculate voltage of individual small piece.

I attached my problem.

 

[BvU]

Hi Gunmo,

Yes, this is a kind of 'lots of capacities in parallel'.
For an ideal conductor, all the material is at the same voltage: if not, then the potential difference would let the charge carriers move until the potential (voltage) is equal everywhere.

 

[Gunmo]

So, to find capacitance of the device, I need to divide the area with small element and C = C1 + C2 + C3...

 

[jim hardy]

The electric field in a capacitor is between its plates.
Since the plates are conductive there can be no field in the direction along their length,
So,
voltage between the plates at any point along their length must be the same, as BvU observed earlier.

But -

That's an interesting example you posed.

Be aware that in deforming the structure work was done while changing the distance between the electrodes.
That's because the opposite charges on the electrodes attract one another.
So when you deformed the plates the Force X Distance product of [ that Coulombic attractive force X distance moved ] has units of work.
That work shows up as a change in voltage across the capacitor.

Charge Q on a capacitor = C_apacitance X V_oltage
You didn't change Q but you did change C_apacitance,
and their ratio is voltage.

Just another little quirk of the universe. Good for "electrical trivial pursuits" parlor games, but don't be surprised if you find it in a physics quiz .

It's good to get your thinking oriented early so that you focus not so much on the plates of a capacitor but on what's in between them.
Watch the electrometer here (about 1:30) indicate increasing voltage as capacitor plates are separated.