Energy stored in the capacitor
Capacitor not only stores the charge but also it stores energy. When a battery is connected to the capacitor, electrons of total charge -Q are transferred from one plate to the other plate. To transfer the charge, work is done by the battery. This work done is stored as electrostatic potential energy in the capacitor.
To transfer an infinitesimal charge dQ for a potential difference V, the work done is given by
This work done is stored as electrostatic potential energy (UE) in the capacitor.
where Q = CV is used. This stored energy is thus directly proportional to the capacitance of the capacitor and the square of the voltage between the plates of the capacitor. But where is this energy stored in the capacitor? To understand this question, the equation (1.87) is rewritten as follows using the results C=ε0A/d and Ed
where Ad = volume of the space between the capacitor plates. The energy stored per unit volume of space is defined as energy density uE =U/Volume From equation (1.88), we get
From equation (1.89), we infer that the energy is stored in the electric field existing between the plates of the capacitor. Once the capacitor is allowed to discharge, the energy is retrieved.
It is important to note that the energy density depends only on the electric field and not on the size of the plates of the capacitor. In fact, expression (1.89) is true for the electric field due to any type of charge configuration.