Let's say you have two infinitely large plates. I understand the formulas for capacitance. What I don't understand is the intuition behind the fact that when you increase the distance between the plates, capacitance decreases. I understand that as you increase distance, potential difference increases, and so based on one of the capacitance formulas, capacitance decreases. That's obvious. But what's the intuitive meaning / significance behind it? The textbook I'm using says "capacitance is a measure of the ability of a capacitor to store energy." That seems to me to go against the idea that as you increase distance, you decrease capacitance, because the further apart the plates are, the more energy is stored between them due the increasing potential difference. If you can answer my question, please do not use formulas. I understand the formulas. I'm really looking for just an intuitive understanding. Also, I think I would understand more if you don't provide an analogy (that's just me).
Thank you in advance.
PS: Sorry I think it's important to distinguish between the case of infinitely large plates and not infinitely large. My question was addressing infinitely large plates. But I would appreciate an explanation on not infinitely large plates as well, and the differences between these two cases.
Best Answer
Infinite plates have a constant electric field (at fixed charge density). Constant electric field means constant voltage gradient, so total voltage increases linearly with distance from the plate.
Capacitance is charge (which is fixed) per volts (which increases with distance); hence: capacitance decreases with distance between the plates.