A capacitor is formed from two parallel metal plates, with air between them, separated by a variable distance $x$, as shown in Fig. 6.1. Since $C$ is inversely proportional to $x$, the capacitor is charged by a supply so that the plates have a potential difference (p.d.) $V$. State expressions, in terms of $C$ and $V$, for the charge $Q$ on one plate and for the energy $E$ stored in the capacitor.
The charged capacitor in (a) is then disconnected from the supply. At the start, the plates are separated by a distance $L$. They are then brought closer by a distance $D$, as shown in Fig. 6.2. State an expression, in terms of $C$, $V$, $L$ and $D$, for the new capacitance $C_N$.
State an expression, in terms of $C$, $V$, $L$ and $D$, for the new charge $Q_N$ on one of the plates.
State an expression, in terms of $C$, $V$, $L$ and $D$, for the new potential difference $V_N$ between the plates.
Explain whether reducing the separation of the plates in (b) causes the energy stored in the capacitor to increase or decrease.