Electrostatic interaction energy between two coaxial parallel uniformly charged disks

We calculate exactly the electrostatic interaction energy between two coaxial parallel uniformly charged infinitely thin disks. For the sake of generality, it is assumed that the disks have different radii and contain different amounts of total electric charge. The results derived when expressed in one-dimensional integral form are very suitable for numerical calculations. An explicit analytical formula is provided for the electrostatic interaction energy between two disks with same radius in terms of a family of special functions known as complete elliptic integrals. The results obtained are applicable to various electrostatic models including the case of a circular parallel plate capacitor