Electricity and magnetism/Electrostatics/The charge of a capacitor

A capacitor is made up of two conductive plates, very close to each other, and separated by an insulating material. Each of the terminals is connected to one of the plates. When the capacitor is turned on, one plate loses some of its electrons and becomes positively charged, while the other plate gains electrons and becomes negatively charged. We prove with Gauss' theorem (in the chapter on Maxwell's equations) that the electric force field produced by an infinite charged plane, whose charge density is uniform and equal to , is also uniform on each side of the charged plane, perpendicular to it, that its magnitude is , if it is surrounded by emptiness, and its direction on each side of the plane is opposed to its direction on the other side. Since the electric field produced by several charges is the sum of the fields produced by each of them, the electric field produced by two parallel charged planes, whose surface charge densities are equal and opposite, is therefore uniform between the planes, perpendicular to them, and its greatness is where is the absolute value of the surface charge density, while it is equal to zero in all the space exterior to the two charged planes. The field produced by a finite surface capacitor is identical to the previous one except at the edges: 400px The work of the electric force on a unit charge between the plates is equal to where is their distance. This remains true for finished plates far from their edges. The voltage between the plates is therefore proportional to their electric charge . The electric charge is therefore proportional to the voltage: where is the capacitance of the capacitor. measures the amount of charge received by one of the plates for a given voltage. for plates of surface separated by vacuum, separated by a distance . Proof: This is why we make capacitors with large surfaces wound on themselves, separated by an insulating film as thin as possible. is the vacuum permittivity. If the plates are separated by an insulating material of permittivity , the capacitance of the capacitor is