Capacitance

Capacitance (measure in Farads) is the ability for a Capacitor for it to hold charge per work needed to bring the charge there:

This definition applies when . It can also be defined using Gauss’s Law. For a parallel plate capacitor:

When the area of the two plates are different, we only use the overlapped area.

For a Coaxial Cylinder on inner radius , outer radius and length , we can employ a similar process using a gaussian surface of radius :

For a concentric sphere capacitor with inner radius and outer radius , we construct a spherical gaussian surface of radius :

In all of these formulas for , we use for vacuum permittivity. When there is another medium, such as a Dielectric, we instead use with a dielectric constant .

The Work done at any instant by a parallel plate capacitor on a charge by a potential difference is:

In other words, the Potential Energy stored in a Capacitor is:

We can also find the Energy Density in The Electric Field between the Plates:

In General: