A parallel plate capacitor consists of two metallic plates placed very close to each other and with surface charge densities σ and -σ respectively. The field lines created by the plates are illustrated separately in the next figure. The magnitude of the electric field due to an infinite thin flat sheet of charge is:
But in a real capacitor the plates are conducting, and the surface charge density will change on each plate when the other plate is brought closer to it. That is, in the limit that the two plates get brought closer together, all of the charge of each plate must be on a single side.
When we find the electric field between the plates of a parallel plate capacitor we assume that the electric field from both plates is E = σ 2ϵ0n.^ E = σ 2 ϵ 0 n. ^ The factor of two in the denominator comes from the fact that there is a surface charge density on both sides of the (very thin) plates.
Electrical field lines in a parallel-plate capacitor begin with positive charges and end with negative charges. The magnitude of the electrical field in the space between the plates is in direct proportion to the amount of charge on the capacitor.
The y axis is into the page in the left panel while the x axis is out of the page in the right panel. We now show that a capacitor that is charging or discharging has a magnetic field between the plates. Figure 17.1.2: shows a parallel plate capacitor with a current i flowing into the left plate and out of the right plate.
Here, the electric field is uniform throughout and its direction is from the positive plate to the negative plate. The potential difference across the capacitor can be calculated by multiplying the electric field and the distance between the planes, given as,