List of top Physics Questions on electrostatic potential and capacitance

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.
Three charges q, q and Q ($q=+20~\mu C$ and $Q=+10~\mu C$) are placed on the circumference of a circle of radius $10\sqrt3$ cm. If the distance between any two charges is same, then the total electrostatic potential energy of the system of the three charges is
The electric potentials at two points A and B are \(+60\text{ V}\) and \(-30\text{ V}\) respectively. If a particle of mass \(20\,\mu\text{g}\) and charge \(+10\,\mu\text{C}\) is released from rest at point A, then the velocity with which the particle reaches point B is:
The INCORRECT formula representing the energy stored in a parallel plate capacitor in usual notation is
In a uniform electric field E, the work done in rotating the electric dipole of dipole moment P from $-45^{\circ}$ to $45^{\circ}$ with respect to the field direction is
Derive the expression for the capacitance of a parallel plate capacitor (with and without dielectric slab).

Two charges \( +q \) and \( -q \) are placed at points \( A \) and \( B \) respectively which are at a distance \( 2L \) apart. \( C \) is the midpoint of \( AB \). The work done in moving a charge \( +Q \) along the semicircle CSD (\( W_1 \)) and along the line CBD (\( W_2 \)) are 

Find work done in bringing charge q = 3nC from infinity to point A as shown in the figure : 

Two capacitors \( C_1 \) and \( C_2 \) are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are \( U_1 \) and \( U_2 \), respectively. Which of the given statements is true?
Two capacitors C1 and C2 are connected in parallel to a battery
A thin pencil of length \( f/4 \) is placed coinciding with the principal axis of a mirror of focal length \( f \). The image of the pencil is real and enlarged, just touches the pencil. Calculate the magnification produced by the mirror.
Two points A and B are located at distances 4 cm and 5 cm respectively from a point charge $+20\mu C$. The work done in taking a charge of $+2\mu C$ from point A to point B is
The charge on a parallel plate capacitor is 200 μC and its capacitance is 4 μF. If the distance between the plates of the capacitor is 2 mm, then the electric force between the plates of the capacitor is
If a charge of 3 nC is placed at each vertex of a cube of side 3 m, then the electric potential at the centre of the cube is:
Three infinitely long wires with linear charge density \( \lambda \) are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?
Two point charges \( +4 \, \mu\text{C} \) and \( -2 \, \mu\text{C} \) are separated by a distance of 0.3 m in air. What is the magnitude of the electrostatic force between them?

The output of the circuit is low (zero) for:

(A) \( X = 0, Y = 0 \) 
(B) \( X = 0, Y = 1 \) 
(C) \( X = 1, Y = 0 \) 
(D) \( X = 1, Y = 1 \) 
Choose the correct answer from the options given below:

Three infinitely long wires with linear charge density \( \lambda \) are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?