Explain the underlying principle of working a parallel plate capacitor. If two similar plates, each of area $A$ having surface charge densities $+\sigma$ and $-\sigma$ are separated by a distance $d$ in air, write expressions for the potential difference between the plates.

Explain the underlying principle of working a parallel plate capacitor. If two similar plates, each of area $A$ having surface charge densities $+\sigma$ and $-\sigma$ are separated by a distance $d$ in air, write expressions for capacity of the capacitor so formed.

Deduce an expression for the electrostatic energy stored in a capacitor of capacitance $C$ and having charge $Q.$ How will the energy stored?

Deduce an expression for the electrostatic energy stored in a capacitor of capacitance $C$ and having charge $Q.$ How will the electric field inside the capacitor be affected when it is completely filled with a dielectric material of dielectric constant ${}^{\text{'}}K^{\text{'}}$?

Explain the principle of a device that can build up high voltages of the order of a few millions volts. Draw a schematic diagram and explain the working of this device. Is there any restriction on the upper limit of the high voltage set up in the machine ? Explain.

A parallel plate air capacitor has capacitance $10\mu \mathrm{F}.$ It is charged by connecting to a $50 \mathrm{V}$ battery. Then it is disconnected from the battery and the space between the two plates of the capacitor is filled with a material having dielectric constant $5.$ Compare

charge,