Spherical capacitor connected to a battery
Based on the experiments carried out by the physicist Petrus van Musschenbroek, who managed to store the electric charge for some time, capacitors emerged, which are devices consisting of two electrified conductors with opposite electric charges and separated by an insulating material. If we look, we will see that capacitors are manufactured in different ways.
But one type that is widely studied is the spherical capacitor. This type of equipment is widely used in experiments with high potential differences. One of these devices that we can mention is the Van de Graaf generator.
Basically, a spherical capacitor is formed, that is, composed of an element with a spherical shape, as shown in the figure above, connected to a high voltage battery. The capacitance of a spherical capacitor depends on the size of its radius R. By mathematical definition we can know the capacitance from the following equation:
We have to be aware of the fact that inside a conductor in electrostatic equilibrium the electric field is zero. Thus, the potential within it is the same, that is, it is constant. The potential can be determined using its capacitance.
This results in:
The potential outside the capacitor, at a distance r (r > R), is the same as a point charge Q placed at the center:
If we put two spherical capacitors in contact, both will have the same potential, redistributing their charges as follows: