Parallel Plate Capacitor Capacitance

Question

Say you have a parallel plate capacitor where the distance between them is 1mm. If you put a metal plate directly in the middle of them with the same area and a thickness of 0.5mm you reduce the 'empty space' for the capacitors to two lots of 0.25mm distances. After doing some calculations you find that the capacitance doubles.

My question is what is the physical reason for the capacitance increasing? I was thinking that it was due to the metal plate storing additional charge hence increasing the capacitance but I am not 100% sure. Any feedback welcome!

Answer 1

The metal plate in the middle does not store any additional charges - it just brings the opposite charges stored on the capacitor plates closer together.

When we insert a $0.5$mm plate in the gap, we, essentially, replace one capacitor with $1$mm gap, by two capacitors with $0.25$mm gaps, connected in series. Since the capacitance of each of these two capacitors is four times larger than the capacitance of the original capacitor, their combined capacitance, as you've pointed out, is twice larger.

We might ask why, in general, the capacitance increases when the gap decreases.

This is because, for a given plate size and charge, assuming a uniform electric field, $E$, in the gap, the voltage between the plates decreases as the plates get closer together (since $V=Ed$). Using the same logic, we can say that, given the applied voltage, a capacitor with a smaller gap can store a greater charge, which, by definition $(C=\frac Q V)$, means that it has a greater capacitance.