Electric Charges and Fields

The electric flux is \(ϕ=\alpha \sigma +\beta \lambda\) where \(\lambda\) and \(\sigma\) are linear and surface charge density, respectively. \(\left(\frac{\alpha }{\beta }\right)\) represents

[JEE Main 2025, 23 Jan (Shift 1)]

A point charge causes an electric flux of \(-2\times {10}^{4}N{m}^{2}{C}^{-1}\) to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is :
(Given \({ϵ}_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}\) )

[JEE Main 2025, 29 Jan (Shift 2)]

Consider a circular loop that is uniformly charged and has a radius \(\mathrm{a}\sqrt{2}\). Find the position along the positive z -axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin :

[JEE Main 2025, 2 Apr (Shift 2)]

Two point charges \({q}_{1}=3\mu C\) and \({q}_{2}=-4\mu C\) are placed at points \((2\hat{i}+3\hat{j}+3\hat{k})\) and \((\hat{i}+\hat{j}+\hat{k})\) respectively. Force on charge \({q}_{2}\) is _________ N. (Take \(\frac{1}{4\pi {ϵ}_{0}}=9\times {10}^{9}\) SI Units)

[JEE Main 2026, 8 Apr (Shift 2)]

An uncharged conducting sphere is brought in contact with an identical sphere having a charge of \(4 \times 10^{-8} \mathrm{C}\). After contact, the spheres are separated and placed at a distance such that the electrostatic force between them is \(9 \times 10^{-3} \mathrm{~N}\). Find the distance between the spheres.

A charged particle of charge Q and mass \(m\) is suspended from a string of length \(l\) in a uniform electric field \(E\)​. If the particle is displaced slightly and released, it undergoes small oscillations. Ignoring gravity, determine the time period of these oscillations.(Shift - I Memory Based)

An electric field is given by \(\left(6\hat{i}+5\hat{j}+3\hat{k}\right)\) N / C. The electric flux through a surface area \(30\hat{i}\) m² lying in YZ-plane (in SI unit) is :

[JEE Main 2024, 29 Jan (Shift 2)]

An electric field is given by \(\left(6\hat{i}+5\hat{j}+3\hat{k}\right)\) N / C. The electric flux through a surface area \(30\hat{i}\) m² lying in YZ-plane (in SI unit) is :

[JEE Main 2024, 29 Jan (Shift 2)]

The ratio of electric force to gravitational force between two particles having charges \({q}_{1}\)​ and \({q}_{2}\)​, and masses \({m}_{1}\) and \({m}_{2}\)​, respectively, is (where the symbols have their usual meanings):

(Shift I Memory Based)

Two metal plates (A, B) are kept horizontally with separation of \(\left(\frac{12}{\pi }\right)cm\), with plate A on the top. An atomizer jet sprays oil (density \(1.5g/c{m}^{3}\) ) droplets of radius 1 mm horizontally. All oil droplets carry a charge 5 nC . The potentials \({V}_{A}\) and \({V}_{B}\) required on plates A and B respectively in order to ensure the droplets do not descend. The values of \({V}_{A}\) and \({V}_{B}\) are _______(Neglect the air resistance to the droplets and take \(g=10m/{s}^{2}\) )

[02 April, 2026 (Shift-2)]

Two small spherical balls of mass 10 g each with charges \(-2\mu \mathrm{C}\) and \(2\mu \mathrm{C}\), are attached to two ends of very light rigid rod of length 20 cm . The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of \(100\mu \mathrm{C}/{\mathrm{m}}^{2}\) such that length of rod makes an angle of \(30^\circ\) with electric field generated by charge sheet. Net torque acting on the rod is:
(Take \({\epsilon }_{0}:8.85\times {10}^{-12}{\mathrm{C}}^{2}/{\mathrm{Nm}}^{2}\))

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field \({\vec{E}}_{1}={E}_{0}\hat{x}\) If another electric field \({\vec{E}}_{2}=2{E}_{0}(\hat{y}+\hat{z})\) is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

[JEE Main 2026, 4 Apr (Shift 2)]

Two identical conducting spheres \(P\) and \(S\) with charge \(Q\) on each, repel each other with a force \(16 \ N\). A third identical uncharged conducting sphere \(R\) is successively brought in contact with the two spheres. The new force of repulsion between \(P\) and \(S\) is :

[JEE Main 2024, 06 Apr (Shift 2)]

Two identical conducting spheres \(P\) and \(S\) with charge \(Q\) on each, repel each other with a force \(16 \ N\). A third identical uncharged conducting sphere \(R\) is successively brought in contact with the two spheres. The new force of repulsion between \(P\) and \(S\) is :

[JEE Main 2024, 06 Apr (Shift 2)]

An electric dipole of mass m, charge q, and length l is placed in a uniform electric field \(\vec{E}={E}_{0}\hat{i}\). When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:

The ratio of electric force to gravitational force between two particles having charges \({\mathrm{q}}_{1},{\mathrm{q}}_{2}\mathrm{and}{\mathrm{m}}_{1}\mathrm{and}{\mathrm{m}}_{2}\)respectively is (where symbols have their usual meanings)

A charge \(\mathrm{q}\) is placed at the center of one of the surface of a cube. The flux linked with the cube is:

A point charge causes an electric flux of \(-2\times {10}^{4}N{m}^{2}{C}^{-1}\) to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is :
(Given \({ϵ}_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}\) )

[JEE Main 2025, 29 Jan (Shift 2)]

The ratio of electric force to gravitational force between two particles having charges \({q}_{1}\)​ and \({q}_{2}\)​, and masses \({m}_{1}\) and \({m}_{2}\)​, respectively, is (where the symbols have their usual meanings):

(Shift I Memory Based)

A dipole with two electric charges of \(2\mu \mathrm{C}\) magnitude each, with separation distance \(0.5\mu \mathrm{m}\), is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of \(5\) V is applied. Separation between the plates is \(0.5\) mm . If the dipole is rotated by \(30^\circ\) from the axis, it tends to realign in the direction due to a torque. The value of torque is :

[JEE Main 2025, 7 Apr (Shift 2)]

An infinitely long wire has uniform linear charge density \(\lambda =2\mathrm{nC}/\mathrm{m}\). The net flux through a Gaussian cube of side length \(\sqrt{3}\mathrm{cm}\), if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be \({\mathrm{xNm}}^{2}{\mathrm{C}}^{-1}\), where x is :
[Neglect any edge effects and use \(\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}\) SI units]

[JEE Main 2025, 8 Apr (Shift 1)]

An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity \({10}^{6}\mathrm{m}/\mathrm{s}\). If the magnitude of the electric field between the plates is \(9.1\mathrm{V}/\mathrm{cm}\), then the vertical component of velocity of electron is (mass of electron \(=9.1\times {10}^{-31}\mathrm{kg}\) and charge of electron \(=1.6\times {10}^{-19}\mathrm{C}\) )

[JEE Main 2025, 22 Jan (Shift 1)]

An uncharged conducting sphere is brought in contact with an identical sphere having a charge of \(4 \times 10^{-8} \mathrm{C}\). After contact, the spheres are separated and placed at a distance such that the electrostatic force between them is \(9 \times 10^{-3} \mathrm{~N}\). Find the distance between the spheres.

An electric dipole of mass m, charge q, and length l is placed in a uniform electric field \(\vec{E}={E}_{0}\hat{i}\). When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:

[JEE Main 2025, 29 Jan (Shift 1)]

The ratio of electric force to gravitational force between two particles having charges \({\mathrm{q}}_{1},{\mathrm{q}}_{2}\mathrm{and}{\mathrm{m}}_{1}\mathrm{and}{\mathrm{m}}_{2}\)respectively is (where symbols have their usual meanings)

Two point charges \(8\mu C\) and \(-2\mu C\) are located at \(x=2\) cm and \(x=4\) cm, respectively on the x-axis, The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is _______.

[02 April, 2026 (Shift-II)]

Force between two point charges \(({q}_{1})\) and \(({q}_{2})\) placed in vacuum at \(r\) cm apart is \(\mathrm{F}\). Force between them when placed in a medium having dielectric constant K = 5 at \(\frac{r}{5}\) cm apart will be:

[JEE Main 2021]

A particle of charge ' \(-q\) ' and mass ' \(m\) ' moves in a circle of radius ' \(r\) ' around an infinitely long line charge of linear charge density ' \(+\lambda\) '. Then time period will be given as :
(Consider \(k\) as Coulomb's constant)

A charged particle of charge Q and mass \(m\) is suspended from a string of length \(l\) in a uniform electric field \(E\)​. If the particle is displaced slightly and released, it undergoes small oscillations. Ignoring gravity, determine the time period of these oscillations.(Shift - I Memory Based)

A point charge causes an electric flux of \(-2\times {10}^{4}N{m}^{2}{C}^{-1}\) to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is :
(Given \({ϵ}_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}\) )

[JEE Main 2025, 29 Jan (Shift 2)]

The electric field at a point on the equatorial plane at a distance \( r \) from the centre of a dipole having dipole moment \( \overrightarrow{\mathrm{P}} \) is given by, ( \( r >> \) separation of two charges forming the dipole, \( \epsilon_{0} \) - permittivity of free space)

[Re-NEET 2020]

An electric dipole of moment \(\vec{p}=(-\hat{i}-3 \hat{j}+2 \hat{k}) \times 10^{-29}\) C.m. is at the origin \((0,0,0)\). The electric field due to this dipole at \(\vec{r}=(+\hat{i}+3 \hat{j}+5 \hat{k})\) (note that \(\vec{r} \cdot \vec{p}=0)\) is parallel to

[JEE Main 2020, 9 Jan (Shift 1)]

If two charges \({q}_{1}\) and \({q}_{2}\) are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?

[JEE Main 2022]

An oil drop of radius \( 2 \ \mathrm{~mm} \) with a density \( 3 \ \mathrm{~g} \mathrm{~cm}^{-3} \) is held stationary under a constant electric field \( 3.55 \) \( \times 10^{5} \ \mathrm{Vm}^{-1} \) in the Millikans oil drop experiment. What is the number of excess electrons that the oil drop will possess?

(consider \( g=9.81 \mathrm{~m} / \mathrm{s}^{2} \) )

[JEE Main 2021, 18 Mar (Shift 1)]

If \({∮}_{s}\vec{E}\cdot \vec{dS}=0\) over a surface, then:

[NEET 2023]

An oil drop of radius \( 2 \mathrm{~mm} \) with a density \( 3 \mathrm{~g} \mathrm{~cm}^{-3} \) is held stationary under a constant electric field \( 3.55 \) \( \times 10^{5} \mathrm{Vm}^{-1} \) in the Millikans oil drop experiment. What is the number of excess electrons that the oil drop will possess?

(consider \( g=9.81 \mathrm{~m} / \mathrm{s}^{2} \) )

[JEE Main 2021, 18 Mar (Shift 1)]

An electron with kinetic energy \(K_1\) enters between parallel plates of a capacitor at angle ' \(\alpha\) ' with the plates. It leaves the plates at angle ' \(\beta\) ' with kinetic energy \(K_2\). Then the ratio of kinetic energies \(K_1: K_2\) will be:

[JEE Main 2021, 25 Feb (Shift 2)]

If two charges q₁ and q₂ are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?

[JEE Main 2023, 24 Jan (Shift 1)]

A 10 μC charge is divided into two parts and placed at 1 cm distance so that the repulsive force between them is maximum. The charges of the two parts are:

[JEE Main 2023, 13 Apr (Shift 2)]

A uniformly charged disc of radius \(R\) having surface charge density \(\sigma\) is placed in the \(x y\) plane with its center at the origin. Find the electric field intensity along the z-axis at a distance \(Z\) from origin:

[JEE Main 2022, 24 June (Shift 1)]

Two charges each of magnitude \(0.01 C\) and separated by a distance of \(0.4 mm\) constitute an electric dipole. If the dipole is placed in an uniform electric field ' \(\overrightarrow{ E }\) ' of 10 dyne/C making \(30^{\circ}\) angle with \(\overrightarrow{ E }\), the magnitude of torque acting on dipole is:

Choose the incorrect statement:
(a) The electric lines of force entering into a Gaussian surface provide negative flux.
(b) A charge ' \(q\) ' is placed at the centre of a cube. The flux through all the faces will be the same.
(c) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero.
(d) When electric field is parallel to a Gaussian surface, it provides a finite non-zero flux.

Choose the most appropriate answer from the options given below

A dipole comprises of two charged particles of identical magnitude \(q\) and opposite in nature. The mass \(m\) of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance \(l\). If the dipole is placed in a uniform electric field \(\vec{E}\); such a way that dipole axis makes a very small angle with the electric field \(\vec{E}\). The angular frequency of the oscillations of the dipole when released is given by:

[JEE Main 2023, 6 Apr (Shift 2)]

Consider the force \(F\) on a charge ' \(q\) ' due to a uniformly charged spherical shell of radius \(R\) carrying charge \(Q\) distributed uniformly over it. Which one of the following statements is true for \(F\), if ' \(q\) ' is placed at distance \(r\) from the center of the shell?