The energy of a charged capacitor is given by the expression ($q$= charge on the conductor and $C$ = its capacity)

Two identical capacitors have same capacitance $C$. One of them is charged to the potential $\mathrm{V}$ and other to the potential $2 \mathrm{~V}$. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is :

A charge of $40\,\mu \,C$ is given to a capacitor having capacitance $C = 10\,\mu \,F$. The stored energy in ergs is

A parallel plate capacitor has circular plates of $10\, cm$ radius separated by an air-gap of $1\, mm$. It is charged by connecting the plates to a $100\, volt$ battery. Then the change in energy stored in the capacitor when the plates are moved to a distance of $1\, cm$ and the plates are maintained in connection with the battery, is

A parallel plate capacitor carries a charge $q$. The distance between the plates is doubled by application of a force. The work done by the force is

A sphere of radius $1\,cm$ has potential of $8000\,V$, then energy density near its surface will be