Redistribution of Charges—

Let us consider two isolated conductors of capacitances C₁ and C₂ carrying charges q₁ and q₂ respectively. Let V₁ and V₂ be their respective potential, then

If after redistribution the new charges on the conductors be q₁’ and q₂’ respectively, then

Energy stored in a Capacitor—

Let we have a capacitor of capacitance ‘C’. if at any moment a charge ‘q’ is present on the plates of capacitor so that a potential difference ‘V’ is developed, then

Capacitance with a Metal (conducting) Slab—

Let we have a capacitor of plate area ‘A’ and separation ‘d’ between the plates, then

Now, we place a metal slab of thickness ‘t’ in between the two plates of capacitor and the electric field in the conducting slab is zero. Hence, the potential difference between the plates is,