Electric Charges and Fields

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.

Two identical small conducting balls \(B _1\) and \(B _2\) are given -7 pC and +4 pC charges respectively. They are brought in contact with a third identical ball \(B _3\) and then separated. If the final charge on each ball is -2 pC , the initial charge on \(B_3\) was

Two charged particles P and Q , having the same charge but different masses \({m}_{P}\) and \({m}_{Q}\), start from rest and travel equal distances in a uniform electric field \(\vec{E}\) in time \({t}_{P}\) and \({t}_{Q}\) respectively. Neglecting the effect of gravity, the ratio \(\left(\frac{{t}_{P}}{{t}_{Q}}\right)\) is :

Two charged particles P and Q , having the same charge but different masses \({m}_{P}\) and \({m}_{Q}\), start from rest and travel equal distances in a uniform electric field \(\vec{E}\) in time \({t}_{P}\) and \({t}_{Q}\) respectively. Neglecting the effect of gravity, the ratio \(\left(\frac{{t}_{P}}{{t}_{Q}}\right)\) is :

Two charged particles P and Q , having the same charge but different masses \({m}_{P}\) and \({m}_{Q}\), start from rest and travel equal distances in a uniform electric field \(\vec{E}\) in time \({t}_{P}\) and \({t}_{Q}\) respectively. Neglecting the effect of gravity, the ratio \(\left(\frac{{t}_{P}}{{t}_{Q}}\right)\) is :

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)]

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

[JEE Main 2024, 30 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)

A thin plastic rod is bent into a circular ring of radius \(R\). It is uniformly charged with charge density \(\lambda\). The magnitude of the electric field at its centre is :

Two identical small conducting balls \(B _1\) and \(B _2\) are given -7 pC and +4 pC charges respectively. They are brought in contact with a third identical ball \(B _3\) and then separated. If the final charge on each ball is -2 pC , the initial charge on \(B_3\) was

A thin plastic rod is bent into a circular ring of radius \(R\). It is uniformly charged with charge density \(\lambda\). The magnitude of the electric field at its centre is :

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:

A metal cube of side \(5\mathrm{cm}\) is charged with \(6\mu \mathrm{C}\). The surface charge density on the cube

Two charges \(\mathrm{q}_1\) and \(\mathrm{q}_2\) are placed at the centres of two spherical conducting shells of radius \(r_1\) and \(r_2\) respectively. The shells are arranged such that their centres are \(d\left[>\left(r_1+r_2\right)\right]\) distance apart. The force on \(q_2\) due to \(\mathrm{q}_1\) is :

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:

A thin plastic rod is bent into a circular ring of radius \(R\). It is uniformly charged with charge density \(\lambda\). The magnitude of the electric field at its centre is :

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 identical small conducting balls \(B _1\) and \(B _2\) are given -7 pC and +4 pC charges respectively. They are brought in contact with a third identical ball \(B _3\) and then separated. If the final charge on each ball is -2 pC , the initial charge on \(B_3\) was

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 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)]

Two charged particles P and Q , having the same charge but different masses \({m}_{P}\) and \({m}_{Q}\), start from rest and travel equal distances in a uniform electric field \(\vec{E}\) in time \({t}_{P}\) and \({t}_{Q}\) respectively. Neglecting the effect of gravity, the ratio \(\left(\frac{{t}_{P}}{{t}_{Q}}\right)\) is :

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 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 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)

\(\text{ The number of electrons for two coulombs of charge is }\)

Spheres A and B having equal masses are given charges +q and -q respectively. If after charging their respective masses are respectively \({m}_{A}\) and \({m}_{B}\), relation of \({m}_{A}and{m}_{B}\) will be

The relative permittivity ( \({ϵ}_{r}\) ) of a medium is hard

Charge on a hollow metallic sphere is 10 coulomb. Radius of the sphere is 5 cm . Electric field inside the sphere will be

[2024]

The electric dipole moment per unit volume of a substance is called:
[PYQ 2024]

Electric charges are uniformly distributed in a small volume. The flux of electric field through a spherical surface of radius 2 cm surrounding the total charge is\(10\mathrm{V}\times \mathrm{m}\). The flux over a sphere of radius 4 cm will be :

[2024]

Beams of electrons and protons move parallel to each other in the same direction. They

According to Gauss' law of electrostatics

An electric dipole of length \(2 \mathrm{~cm}\) is placed at an angle of \(30^{\circ}\) with an electric field \(2 \times 10^5 \mathrm{~N} / \mathrm{C}\). If the dipole experiences a torque of \(8 \times 10^{-3} \mathrm{Nm}\), the magnitude of either charge of the dipole, is

Assertion (A) : Work done in moving a charge around a closed path, in an electric field is always zero.

Reason (R) : Electrostatic force is a conservative force.

A point charge situated at a distance ' \(r\) ' from a short electric dipole on its axis, experiences a force \(\vec{F}\). If the distance of the charge is ' \(2 r\) ', the force on the charge will be :

Which one of the following is not a scalar quantity?

The magnitude of the electric field due to a point charge object at a distance of \(4.0 m\) is \(9 N / C\). From the same charged object the electric field of magnitude, \(16 \frac{ N }{ C }\) will be at a distance of