Monday, December 31, 2012

Parallel Plate Capacitor

A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance.

Let A be the area of each plate and d the separation between them. The two plates have charges Q and –Q.

Since d is much smaller than the linear dimension of the plates (d2 << A), we can use the result on electric field by an infinite plane sheet of uniform surface charge density.

Plate 1 has surface charge density σ = Q/A and plate 2 has a surface charge density –σ. The electric field in different regions is:

Outer region I (region above the plate 1),

The direction of electric field is from the positive to the negative plate.

Thus, the electric field is localised between the two plates and is uniform throughout. For plates with finite area, this will not be true near the outer boundaries of the plates. The field lines bend outward at the edges – an effect called ‘fringing of the field’.

Now for uniform electric field, potential difference is simply the electric field times the distance between the plates, that is,