List of top Physics Questions on electrostatic potential and capacitance asked in UP Board XII

Explain the meaning of the electrical capacity of a conductor. How capacity of a conductor can be increased?

Compute the electric potential energy of the system with the help of the figure given above. The square has side 1 cm with charges \(+1\ \mu C\) and \(+1\ \mu C\) on the two top corners and \(-1\ \mu C\) and \(-1\ \mu C\) on the two bottom corners.
OR
The capacitance of a parallel plate capacitor is 20 pF and distance between the plates is 4 mm. It is charged by a battery of 100 volt and then battery is removed. Now a dielectric slab (K = 4) and 2 mm thickness is placed in between the plates. Find out: (i) the final charge on each plate (ii) the potential difference between the plates.

What is an equipotential surface?

Prove that the energy density inside a charged capacitor is \( \tfrac{1}{2}\varepsilon_0 E^2 \).

Deduce the formula of equivalent capacity of three condensers connected in parallel.

The area of each plate of a parallel plate condenser is 100 cm² and the intensity of the electric field between the two plates is 100 newton/coulomb. How much charge is there on each plate?
(Take \( \varepsilon_0 = 8.85\times10^{-12}\ \text{C}^2/\text{N·m}^2 \).)

Prove that the electric potential energy per unit volume of a charged condenser is \(\tfrac{1}{2}\varepsilon_0 E^2\), where symbols have their usual meaning.

Derive the formula for energy loss on connecting two charged conductors through a conducting wire.
OR
Explain the meaning of polarization of a dielectric material. What will be the effect on the capacity of an air filled parallel plate capacitor on putting a dielectric material in between its plates? Equivalent capacity of two condensers in series is 7.5 µF and in parallel is 30 µF. What will be the capacity of both the capacitors separately?

Assuming Earth as a spherical conductor of diameter 12,800 km, calculate its capacity.