Energy Stored in a Capacitor

A condenser of certain capacity is charged to a potential V and stores some energy. A second condenser of twice the capacity is to store the half the energy of first, find to what potential one must be charged?

Two capacitor A and B of capacities $C$ and $2C$ are connected in parallel and the combination of is connected to a battery of $V$ volts. After the charging is over, the battery is removed. Now a dielectric slab of $K = 2$ is inserted between the plates of A so as to fill the space completely. The energy lost by the system during the sharing of charges is ?

An elementary particle of mass m and charge +e initially at very large distance is projected with velocity v at a much more massive particle +Ze at rest. The closest possible distance of approach of the incident particle is 

Derive an expression for the energy stored in a capacitor. What is the energy stored when space between the plates is filled with a dielectric, with charging battery connected in the circuit.

Derive an expression for the energy stored in a capacitor. What is the energy stored when space between the plates is filled with a dielectric, with charging battery disconnected.

A $4 \mathrm{\mu F}$ capacitor is charged by a $200 \mathrm{V}$ supply. It is then disconnected from the supply and is connected to another uncharged $2 \mathrm{\mu F}$ capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?

The plates of a parallel plate capacitor have an area of $90 {\mathrm{cm}}^2$ each and are separated by $2.5 \mathrm{mm}$. The capacitor is charged by connecting it to a $400 \mathrm{V}$ supply. How much electrostatic energy is stored by the capacitor? View this energy as electrostatic field stored between the plates of capacitor, energy per unit volume, $\mathrm{u}$. Hence arrive at a relation between $\mathrm{u}$ and magnitude of electric field $\mathrm{E}$ between the plates.

A $600 \mathrm{pF}$ capacitor is charged by a $200 \mathrm{V}$ supply. It is then disconnected from the supply and is connected to another uncharged $600 \mathrm{pF}$ capacitor. How much electrostatic energy is lost in the process?

A $12 \mathrm{pF}$ capacitor is connected to a $50 \mathrm{V}$ battery. How much electrostatic energy is stored in the capacitor?