Electrostatic Potential and Capacitance

A capacitor with capacitance \(1 \mu \mathrm{~F}\) is connected to a 20 V supply. The distance between the plates is 1 \(\mu \mathrm{m}\). Find the energy density between the plates.

(Shift - II Memory Based)

Two charges \(+q\) each are kept ' \(2 a\) ' distance apart. A third charge \(-2 q\) is placed midway between them. The potential energy of the system is -

The value of electric potential at a distance of 9 cm from the point charge \(4\times {10}^{-7}\mathrm{C}\) is [Given \(\left.\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}{\mathrm{Nm}}^{2}{\mathrm{C}}^{-2}\right]\) :

A capacitor \(C_1=6 \mu \mathrm{~F}\), initially charged with a cell of emf 5 V is disconnected and connected to another capacitor \(C_2=12 \mu \mathrm{~F}\) which is initially neutral. The charges on \(C_1\) and \(C_2\) after connection are

(Shift - II Memory Based)

A parallel plate capacitor of capacitance \(40\text{ }\mu F\) is connected to a \(100\text{ }\text{V}\) power supply. The intermediate space between the plates is then filled with a dielectric material of dielectric constant \(K=2\). Calculate the extra charge stored in the capacitor and the change in its electrostatic energy due to the introduction of the dielectric. (JEE Mains - 21 Jan 2025 - Shift I Memory Based)

Parallel plate capacitor was made with two rectangular plates, each with a length of 𝑙=3 cm and breath of b=1 cm. The distance between the plates is 3𝜇 m. Out of the following, which are the ways to increase the capacitance by a factor of 10 ?
A. 𝑙=30 cm, b=1 cm, d=1𝜇 m
B. 𝑙=3 cm, b=1 cm, d=30𝜇 m
C. 𝑙=6 cm, b=5 cm, d=3𝜇 m
D. 𝑙=1 cm, b=1 cm, d=10𝜇 m
E. 𝑙=5 cm, b=2 cm, d=1𝜇 m
Choose the correct answer from the options given below:

Consider a group of charges \(q_1, q_2, q_3 \ldots\) such that \(\Sigma q \neq 0\). Then equipotentials at a large distance, due to this group are approximately :

A proton is taken from point \(P_1\) to point \(P_2\), both located in an electric field. The potentials at points \(P_1\) and \(P_2\) are -5 V and +5 V respectively. Assuming that kinetic energies of the proton at points \(P _1\) and \(P _2\) are zero, the work done on the proton is :

A proton is taken from point \(P_1\) to point \(P_2\), both located in an electric field. The potentials at points \(P_1\) and \(P_2\) are -5 V and +5 V respectively. Assuming that kinetic energies of the proton at points \(P _1\) and \(P _2\) are zero, the work done on the proton is :

The electrostatic potential due to an electric dipole at a distance ' \(r\) ' varies as :

[JEE Main 2024, 30 Jan (Shift 1)]

Two charges \(7\mu \mathrm{c}\) and \(-4\mu \mathrm{c}\) are placed at \((-7\mathrm{cm},0,0)\) and \((7\mathrm{cm},0,0)\) respectively. Given, \({ϵ}_{0}=8.85\times {10}^{-12}{\mathrm{C}}^{2}{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}\), the electrostatic potential energy of the charge configuration is :

[JEE Main 2025, 23 Jan (Shift 2)]

Consider a parallel plate capacitor of area A (of each plate) and separation '𝑑' between the plates. If 𝐸 is the electric field and \({\epsilon }_{0}\) is the permittivity of free space between the plates, then potential energy stored in the capacitor is

[JEE Main 2025, 24 Jan (Shift 1)]

A parallel plate capacitor is charged by a battery. The battery is then disconnected and the plates of the charged capacitor are then moved farther apart. In the process :

Ten capacitors, each of capacitance \(1 \mu F\), are connected in parallel to a source of 100 V . The total energy stored in the system is equal to :

Consider a group of charges \(q_1, q_2, q_3 \ldots\) such that \(\Sigma q \neq 0\). Then equipotentials at a large distance, due to this group are approximately :

The capacitance of a capacitor with charge \(\mathrm{q}\) and a potential difference \(V\) depends on :

Two charges \(+q\) each are kept ' \(2 a\) ' distance apart. A third charge \(-2 q\) is placed midway between them. The potential energy of the system is -

Parallel plate capacitor was made with two rectangular plates, each with a length of 𝑙=3 cm and breath of b=1 cm. The distance between the plates is 3𝜇 m. Out of the following, which are the ways to increase the capacitance by a factor of 10 ?
A. 𝑙=30 cm, b=1 cm, d=1𝜇 m
B. 𝑙=3 cm, b=1 cm, d=30𝜇 m
C. 𝑙=6 cm, b=5 cm, d=3𝜇 m
D. 𝑙=1 cm, b=1 cm, d=10𝜇 m
E. 𝑙=5 cm, b=2 cm, d=1𝜇 m
Choose the correct answer from the options given below:

The point \(A\) is situated on the axis of a dipole at a distance \(r\) from the dipole, where the electric field and potential are given as \({E}_{0}\)​ and \({V}_{0}\)​, respectively. Find the electric field and potential at point \(B\), which is at a distance \(2r\) from the dipole on its perpendicular bisector.

(Shift II Memory Based)​​

Consider a group of charges \(q_1, q_2, q_3 \ldots\) such that \(\Sigma q \neq 0\). Then equipotentials at a large distance, due to this group are approximately :

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?

[JEE Main 2025, 28 Jan (Shift 1)]

Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 μC are combined to form a bigger drop. The ratio of surface charge density of bigger drop to the smaller drop will be:

[

Two point charges \(-4 \mu c\) and \(4 \mu c\), constituting an electric dipole, are placed at \((-9,0,0)\mathrm{cm}\)and \((9,0,0) \mathrm{cm}\) in a uniform electric field of strength \({10}^{4}{\mathrm{NC}}^{-1}\). The work done on the dipole in rotating it from the equilibrium through \(180^\circ\) is :

[JEE Main 2025, 23 Jan (Shift 2)]

A parallel plate capacitor is charged by a battery. The battery is then disconnected and the plates of the charged capacitor are then moved farther apart. In the process :

Ten capacitors, each of capacitance \(1 \mu F\), are connected in parallel to a source of 100 V . The total energy stored in the system is equal to :

Ten capacitors, each of capacitance \(1 \mu F\), are connected in parallel to a source of 100 V . The total energy stored in the system is equal to :

Two charges \(+q\) each are kept ' \(2 a\) ' distance apart. A third charge \(-2 q\) is placed midway between them. The potential energy of the system is -

The potential of a large liquid drop when eight liquid drops are combined is 20 V. Then, the potential of each single drop was:

Two particles A and B of the same mass but having charges \(q\) and \(4q\) respectively, are accelerated from rest through different potential differences \({V}_{A}\) and \({V}_{B}\) such that they attain same kinetic energies. The value of \(\left(\frac{{V}_{A}}{{V}_{B}}\right)\) is :

A uniform wire of linear charge density \(\lambda\) is placed along the y-axis. Determine the locus of the equipotential surface in the surrounding space.

(Shift - I Memory Based)

Two particles A and B of the same mass but having charges \(q\) and \(4q\) respectively, are accelerated from rest through different potential differences \({V}_{A}\) and \({V}_{B}\) such that they attain same kinetic energies. The value of \(\left(\frac{{V}_{A}}{{V}_{B}}\right)\) is :

Two charges +7 C and - 4 C are located at (-7, 0, 0) m and (7, 0, 0) m, find electrostatic potential energy of the system. \(( K=9 \times 10^9 SI units )\)

(Shift - II Memory Based)

In a parallel-plate capacitor, the length and width of the plates are \(3\text{ }\text{cm}\) and \(1\text{ }\text{cm}\), respectively. The separation between the plates is \(3\text{ }\mu \text{m}\). By which of the following configurations does the capacitance increase by a factor of 10?

(A): \(l=6\text{ }\text{cm},b=5\text{ }\text{cm},d=3\text{ }\mu \text{m}\)
(B): \(l=5\text{ }\text{cm},b=2\text{ }\text{cm},d=1\text{ }\mu \text{m}\)
(C): \(l=5\text{ }\text{cm},b=1\text{ }\text{cm},d=30\text{ }\mu \text{m}\)
(D): \(l=1\text{ }\text{cm},b=1\text{ }\text{cm},d=30\text{ }\mu \text{m}\)

(Shift I Memory Based)

A uniform wire of linear charge density \(\lambda\) is placed along the y-axis. Determine the locus of the equipotential surface in the surrounding space.

(Shift - I Memory Based)

A capacitor \(C_1=6 \mu \mathrm{~F}\), initially charged with a cell of emf 5 V is disconnected and connected to another capacitor \(C_2=12 \mu \mathrm{~F}\) which is initially neutral. The charges on \(C_1\) and \(C_2\) after connection are

(Shift - II Memory Based)

Two particles A and B of the same mass but having charges \(q\) and \(4q\) respectively, are accelerated from rest through different potential differences \({V}_{A}\) and \({V}_{B}\) such that they attain same kinetic energies. The value of \(\left(\frac{{V}_{A}}{{V}_{B}}\right)\) is :

A proton is taken from point \(P_1\) to point \(P_2\), both located in an electric field. The potentials at points \(P_1\) and \(P_2\) are -5 V and +5 V respectively. Assuming that kinetic energies of the proton at points \(P _1\) and \(P _2\) are zero, the work done on the proton is :

If the distance between two parallel plates of a capacitor is \(d\), \(A\) is the area of each plate, and \(E\) is the electric field, find the energy stored in the capacitor.

(Shift I - Memory Based)

A parallel plate capacitor is charged by a battery. The battery is then disconnected and the plates of the charged capacitor are then moved farther apart. In the process :

Two particles A and B of the same mass but having charges \(q\) and \(4q\) respectively, are accelerated from rest through different potential differences \({V}_{A}\) and \({V}_{B}\) such that they attain same kinetic energies. The value of \(\left(\frac{{V}_{A}}{{V}_{B}}\right)\) is :

If the distance between two plates of a parallel plate capacitor is halved, its capacity

The capacitors, each of \(4 \mu \mathrm{F}\) are to be connected in such a way that the effective capacitance of the combination is \(6 \mu \mathrm{F}\). This can be achieved by connecting

A point \(P\) lies at a distance \(x\) from the mid point of an electric dipole on its axis. The electric potential at point \(P\) is proportional to

An electron experiences a force \(\left(1.6 \times 10^{-16} N \right) \hat{ i }\) in an electric field \(\overrightarrow{ E }\). The electric field \(\overrightarrow{ E }\) is :