MCQ (Single Correct Answer)

1

Two metal spheres of radius R and 3R have same surface charge density σ. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes σ1 and σ2, respectively. The ratio $ \frac{\sigma_1}{\sigma_2} $ is

JEE Main 2025 (Online) 8th April Evening Shift
2

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion A : Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen.

Reason R : Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell.

In the light of the above statements, choose the correct answer from the options given below.

JEE Main 2025 (Online) 8th April Evening Shift
3

Electric charge is transferred to an irregular metallic disk as shown in the figure. If $\sigma_1$, $\sigma_2$, $\sigma_3$ and $\sigma_4$ are charge densities at given points then, choose the correct answer from the options given below:

JEE Main 2025 (Online) 8th April Evening Shift Physics - Electrostatics Question 17 English

A. $\sigma_1>\sigma_3 ; \sigma_2=\sigma_4$

B. $\sigma_1>\sigma_2 ; \sigma_3>\sigma_4$

C. $\sigma_1>\sigma_3>\sigma_2=\sigma_4$

D. $\sigma_1<\sigma_3<\sigma_2=\sigma_4$

E. $\sigma_1=\sigma_2=\sigma_3=\sigma_4$

JEE Main 2025 (Online) 8th April Evening Shift
4

An infinitely long wire has uniform linear charge density $\lambda = 2 \text{ nC/m}$. The net flux through a Gaussian cube of side length $\sqrt{3}$ cm, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be $x \text{ Nm}^2\text{C}^{-1}$, where $x$ is:

[Neglect any edge effects and use $\frac{1}{4\pi \epsilon_0} = 9 \times 10^9$ SI units]

JEE Main 2025 (Online) 8th April Evening Shift
5

A dipole with two electric charges of 2 µC magnitude each, with separation distance 0.5 µm, 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° from the axis, it tends to realign in the direction due to a torque. The value of torque is:

JEE Main 2025 (Online) 7th April Evening Shift
6

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The outer body of an aircraft is made of metal which protects persons sitting inside from lightning strikes.

Reason (R) : The electric field inside the cavity enclosed by a conductor is zero.

In the light of the above statements, choose the most appropriate answer from the options given below :

JEE Main 2025 (Online) 7th April Evening Shift
7

If $\epsilon_0$ denotes the permittivity of free space and $\Phi_E$ is the flux of the electric field through the area bounded by the closed surface, then dimensions of $\left(\epsilon_0 \frac{d \phi_E}{d t}\right)$ are that of :

JEE Main 2025 (Online) 7th April Morning Shift
8

Two charges $q_1$ and $q_2$ are separated by a distance of 30 cm . A third charge $q_3$ initially at ' C ' as shown in the figure, is moved along the circular path of radius 40 cm from C to D . If the difference in potential energy due to movement of $q_3$ from C to D is given by $\frac{q_3 \mathrm{~K}}{4 \pi \epsilon_0}$, the value of K is :

JEE Main 2025 (Online) 7th April Morning Shift Physics - Electrostatics Question 6 English

JEE Main 2025 (Online) 7th April Morning Shift
9

A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc $A B$ at ' $O$ ' is ' $E$ ' in magnitude. What would be the magnitude of electric field at ' O ' due to arc ABC ?

JEE Main 2025 (Online) 4th April Evening Shift Physics - Electrostatics Question 3 English
JEE Main 2025 (Online) 4th April Evening Shift
10

Two infinite identical charged sheets and a charged spherical body of charge density ' $\rho$ ' are arranged as shown in figure. Then the correct relation between the electrical fields at $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D points is:

JEE Main 2025 (Online) 4th April Morning Shift Physics - Electrostatics Question 2 English

JEE Main 2025 (Online) 4th April Morning Shift
11

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 $\varepsilon_{\mathrm{o}}: 8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2$ )

JEE Main 2025 (Online) 4th April Morning Shift
12

The electrostatic potential on the surface of uniformly charged spherical shell of radius $\mathrm{R}=10 \mathrm{~cm}$ is 120 V . The potential at the centre of shell, at a distance $\mathrm{r}=5 \mathrm{~cm}$ from centre, and at a distance $\mathrm{r}=15$ cm from the centre of the shell respectively, are:

JEE Main 2025 (Online) 3rd April Morning Shift
13

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field.

Reason (R) : In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions.

In the light of the above statements, choose the most appropriate answer from the options given below :

JEE Main 2025 (Online) 2nd April Evening Shift
14
Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is V . The potential difference between the points A and $B$ (shown in the figure) is :JEE Main 2025 (Online) 2nd April Evening Shift Physics - Electrostatics Question 9 English
JEE Main 2025 (Online) 2nd April Evening Shift
15
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 $x y$ plane at the origin :
JEE Main 2025 (Online) 2nd April Evening Shift
16

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density $+\sigma$ and $-2 \sigma$. The force experienced by a point charge +q placed at the mid point between two plates will be:

JEE Main 2025 (Online) 2nd April Morning Shift Physics - Electrostatics Question 14 English

JEE Main 2025 (Online) 2nd April Morning Shift
17

A point charge $+q$ is placed at the origin. A second point charge $+9 q$ is placed at ($\mathrm{d}, 0,0$) in Cartesian coordinate system. The point in between them where the electric field vanishes is:

JEE Main 2025 (Online) 2nd April Morning Shift
18

A small bob of mass 100 mg and charge $+10 \mu \mathrm{C}$ is connected to an insulating string of length 1 m . It is brought near to an infinitely long non-conducting sheet of charge density ' $\sigma$ ' as shown in figure. If string subtends an angle of $45^{\circ}$ with the sheet at equilibrium the charge density of sheet will be.

(Given, $\epsilon_0=8.85 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}$ and acceleration due to gravity, $\mathrm{g}=10 \frac{\mathrm{~m}}{\mathrm{~s}^2}$ )

JEE Main 2025 (Online) 2nd April Morning Shift Physics - Electrostatics Question 13 English

JEE Main 2025 (Online) 2nd April Morning Shift
19

A point charge causes an electric flux of $-2 \times 10^4 \mathrm{Nm}^2 \mathrm{C}^{-1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is :

(Given $\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ )

JEE Main 2025 (Online) 29th January Evening Shift
20

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density $\sigma_{\mathrm{o}}$. Choose the correct option from the following.

JEE Main 2025 (Online) 29th January Evening Shift Physics - Electrostatics Question 36 English
JEE Main 2025 (Online) 29th January Evening Shift
21

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 (Online) 29th January Morning Shift
22

Match List - I with List - II.

List - I List - II
(A) Electric field inside (distance r > 0 from center) of a uniformly charged spherical shell with surface charge density σ, and radius R. (I) σ/ε0
(B) Electric field at distance r>0 from a uniformly charged infinite plane sheet with surface charge density σ. (II) σ/2ε0
(C) Electric field outside (distance r>0 from center) of a uniformly charged spherical shell with surface charge density σ, and radius R. (III) 0
(D) Electric field between 2 oppositely charged infinite plane parallel sheets with uniform surface charge density σ. (IV) $\frac{\sigma}{\epsilon_0 r^2}$

Choose the correct answer from the options given below :

JEE Main 2025 (Online) 29th January Morning Shift
23

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

JEE Main 2025 (Online) 28th January Morning Shift
24

A particle of mass ' $m$ ' and charge ' $q$ ' is fastened to one end ' $A$ ' of a massless string having equilibrium length $l$, whose other end is fixed at point ' $O$ '. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the $x$-axis is

JEE Main 2025 (Online) 28th January Morning Shift Physics - Electrostatics Question 20 English

JEE Main 2025 (Online) 28th January Morning Shift
25

A small uncharged conducting sphere is placed in contact with an identical sphere but having $4 \times 10^{-8} \mathrm{C}$ charge and then removed to a distance such that the force of repulsion between them is $9 \times 10^{-3} \mathrm{~N}$. The distance between them is (Take $\frac{1}{4 \pi \epsilon_{\mathrm{o}}}$ as $9 \times 10^9$ in SI units)

JEE Main 2025 (Online) 24th January Evening Shift
26

JEE Main 2025 (Online) 24th January Evening Shift Physics - Electrostatics Question 22 English

In the first configuration (1) as shown in the figure, four identical charges $\left(q_0\right)$ are kept at the corners A, B, C and D of square of side length ' $a$ '. In the second configuration (2), the same charges are shifted to mid points $G, E, H$ and $F$, of the square. If $K=\frac{1}{4 \pi \epsilon_0}$, the difference between the potential energies of configuration (2) and (1) is given by :

JEE Main 2025 (Online) 24th January Evening Shift
27

Consider a parallel plate capacitor of area A (of each plate) and separation ' $d$ ' between the plates. If $E$ is the electric field and $\varepsilon_0$ is the permittivity of free space between the plates, then potential energy stored in the capacitor is

JEE Main 2025 (Online) 24th January Morning Shift
28

Two point charges $-4 \mu \mathrm{c}$ and $4 \mu \mathrm{c}$, 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 (Online) 23rd January Evening Shift
29

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, $\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$, the electrostatic potential energy of the charge configuration is :

JEE Main 2025 (Online) 23rd January Evening Shift
30

A point particle of charge $Q$ is located at $P$ along the axis of an electric dipole 1 at a distance $r$ as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r. The dipoles are made of opposite charge q separated by a distance $2 a$. For the charge particle at P not to experience any net force, which of the following correctly describes the situation?

JEE Main 2025 (Online) 23rd January Morning Shift Physics - Electrostatics Question 28 English

JEE Main 2025 (Online) 23rd January Morning Shift
31

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

JEE Main 2025 (Online) 23rd January Morning Shift
32

For a short dipole placed at origin O , the dipole moment P is along $x$-axis, as shown in the figure. If the electric potential and electric field at $A$ are $V_0$ and $E_0$, respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the $y$-axis is given by

JEE Main 2025 (Online) 22nd January Evening Shift Physics - Electrostatics Question 31 English

JEE Main 2025 (Online) 22nd January Evening Shift
33

A line charge of length $\frac{\mathrm{a}}{2}$ is kept at the center of an edge $B C$ of a cube ABCDEFGH having edge length ' $a$ ' as shown in the figure. If the density of line charge is $\lambda \mathrm{C}$ per unit length, then the total electric flux through all the faces of the cube will be ___________ . (Take, $\epsilon_0$ as the free space permittivity)

JEE Main 2025 (Online) 22nd January Morning Shift Physics - Electrostatics Question 33 English

JEE Main 2025 (Online) 22nd January Morning Shift
34

Five charges $$+q,+5 q,-2 q,+3 q$$ and $$-4 q$$ are situated as shown in the figure. The electric flux due to this configuration through the surface $$S$$ is :

JEE Main 2024 (Online) 9th April Evening Shift Physics - Electrostatics Question 52 English

JEE Main 2024 (Online) 9th April Evening Shift
35

Two charged conducting spheres of radii $$a$$ and $$b$$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

JEE Main 2024 (Online) 8th April Morning Shift
36

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

JEE Main 2024 (Online) 6th April Evening Shift
37

$$\sigma$$ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is :

JEE Main 2024 (Online) 6th April Morning Shift
38

The vehicles carrying inflammable fluids usually have metallic chains touching the ground:

JEE Main 2024 (Online) 5th April Evening Shift
39

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :

JEE Main 2024 (Online) 5th April Morning Shift
40

A charge $$q$$ is placed at the center of one of the surface of a cube. The flux linked with the cube is:

JEE Main 2024 (Online) 4th April Evening Shift
41

An infinitely long positively charged straight thread has a linear charge density $$\lambda \mathrm{~Cm}^{-1}$$. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is :

JEE Main 2024 (Online) 4th April Morning Shift
42
$C_1$ and $C_2$ are two hollow concentric cubes enclosing charges $2 Q$ and $3 Q$ respectively as shown in figure. The ratio of electric flux passing through $C_1$ and $C_2$ is :

JEE Main 2024 (Online) 1st February Evening Shift Physics - Electrostatics Question 69 English
JEE Main 2024 (Online) 1st February Evening Shift
43

Force between two point charges $$q_1$$ and $$q_2$$ placed in vacuum at '$$r$$' cm apart is $$F$$. Force between them when placed in a medium having dielectric constant $$K=5$$ at '$$r / 5$$' $$\mathrm{cm}$$ apart will be:

JEE Main 2024 (Online) 31st January Evening Shift
44

Two charges $$q$$ and $$3 q$$ are separated by a distance '$$r$$' in air. At a distance $$x$$ from charge $$q$$, the resultant electric field is zero. The value of $$x$$ is :

JEE Main 2024 (Online) 31st January Morning Shift
45

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)

JEE Main 2024 (Online) 30th January Evening Shift
46

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

JEE Main 2024 (Online) 30th January Morning Shift
47

An electric field is given by $$(6 \hat{i}+5 \hat{j}+3 \hat{k}) \mathrm{N} / \mathrm{C}$$. The electric flux through a surface area $$30 \hat{i} \mathrm{~m}^2$$ lying in YZ-plane (in SI unit) is :

JEE Main 2024 (Online) 29th January Evening Shift
48

Two charges of $$5 Q$$ and $$-2 Q$$ are situated at the points $$(3 a, 0)$$ and $$(-5 a, 0)$$ respectively. The electric flux through a sphere of radius '$$4 a$$' having center at origin is :

JEE Main 2024 (Online) 29th January Morning Shift
49

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero.

Reason (R) : Electric lines of forces are always perpendicular to equipotential surfaces.

In the light of the above statements, choose the most appropriate answer from the options given below :

JEE Main 2024 (Online) 27th January Evening Shift
50

An electric charge $$10^{-6} \mu \mathrm{C}$$ is placed at origin $$(0,0)$$ $$\mathrm{m}$$ of $$\mathrm{X}-\mathrm{Y}$$ co-ordinate system. Two points $$\mathrm{P}$$ and $$\mathrm{Q}$$ are situated at $$(\sqrt{3}, \sqrt{3}) \mathrm{m}$$ and $$(\sqrt{6}, 0) \mathrm{m}$$ respectively. The potential difference between the points $\mathrm{P}$ and $\mathrm{Q}$ will be :

JEE Main 2024 (Online) 27th January Morning Shift
51
The electric field due to a short electric dipole at a large distance $(r)$ from center of dipole on the equatorial plane varies with distance as :
JEE Main 2023 (Online) 15th April Morning Shift
52

A $$10 ~\mu \mathrm{C}$$ charge is divided into two parts and placed at $$1 \mathrm{~cm}$$ distance so that the repulsive force between them is maximum. The charges of the two parts are:

JEE Main 2023 (Online) 13th April Evening Shift
53

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

JEE Main 2023 (Online) 13th April Morning Shift
54

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : If an electric dipole of dipole moment $$30 \times 10^{-5} ~\mathrm{C} ~\mathrm{m}$$ is enclosed by a closed surface, the net flux coming out of the surface will be zero.

Reason R : Electric dipole consists of two equal and opposite charges.

In the light of above, statements, choose the correct answer from the options given below.

JEE Main 2023 (Online) 12th April Morning Shift
55

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

JEE Main 2023 (Online) 10th April Evening Shift
56

Electric potential at a point '$$\mathrm{P}$$' due to a point charge of $$5 \times 10^{-9} \mathrm{C}$$ is $$50 \mathrm{~V}$$. The distance of '$$\mathrm{P}$$' from the point charge is:

(Assume, $$\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{+9} ~\mathrm{Nm}^{2} \mathrm{C}^{-2}$$ )

JEE Main 2023 (Online) 8th April Evening Shift
57

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $$\mathrm{R}$$, with distance $$r$$ from the centre O is represented by:

JEE Main 2023 (Online) 8th April Morning Shift Physics - Electrostatics Question 72 English

JEE Main 2023 (Online) 8th April Morning Shift
58

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 '$$\bar{E}$$'; in such a way that dipole axis makes a very small angle with the electric field, '$$\bar{E}$$'. The angular frequency of the oscillations of the dipole when released is given by:

JEE Main 2023 (Online) 6th April Evening Shift
59

For a uniformly charged thin spherical shell, the electric potential (V) radially away from the centre (O) of shell can be graphically represented as -

JEE Main 2023 (Online) 6th April Morning Shift Physics - Electrostatics Question 71 English

JEE Main 2023 (Online) 6th April Morning Shift
60

Let $$\sigma$$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region $$E_{I}, E_{I I}$$ and $$E_{I I I}$$ are:

JEE Main 2023 (Online) 1st February Morning Shift Physics - Electrostatics Question 102 English

JEE Main 2023 (Online) 1st February Morning Shift
61
Considering a group of positive charges, which of the following statements is correct ?
JEE Main 2023 (Online) 31st January Evening Shift
62

Which of the following correctly represents the variation of electric potential $$(\mathrm{V})$$ of a charged spherical conductor of radius $$(\mathrm{R})$$ with radial distance $$(\mathrm{r})$$ from the center?

JEE Main 2023 (Online) 31st January Morning Shift
63
As shown in the figure, a point charge $Q$ is placed at the centre of conducting spherical shell of inner radius $a$ and outer radius $b$. The electric field due to charge $\mathrm{Q}$ in three different regions $\mathrm{I}, \mathrm{II}$ and $\mathrm{III}$ is given by:

$(\mathrm{I}: r < a, \mathrm{II}: a < r < b$, III: $r>b$ )

JEE Main 2023 (Online) 30th January Evening Shift Physics - Electrostatics Question 98 English
JEE Main 2023 (Online) 30th January Evening Shift
64

Electric field in a certain region is given by $$\overrightarrow{\mathrm{E}}=\left(\frac{\mathrm{A}}{x^{2}} \hat{i}+\frac{\mathrm{B}}{y^{3}} \hat{j}\right) \text {. The } \mathrm{SI} \text { unit of } \mathrm{A} \text { and } \mathrm{B}$$ are :

JEE Main 2023 (Online) 30th January Morning Shift
65

Two isolated metallic solid spheres of radii $$\mathrm{R}$$ and $$2 \mathrm{R}$$ are charged such that both have same charge density $$\sigma$$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $$\sigma^{\prime}$$. The ratio $$\frac{\sigma^{\prime}}{\sigma}$$ is :

JEE Main 2023 (Online) 30th January Morning Shift
66

A point charge $$2\times10^{-2}~\mathrm{C}$$ is moved from P to S in a uniform electric field of $$30~\mathrm{NC^{-1}}$$ directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work done by electric field will be

JEE Main 2023 (Online) 29th January Evening Shift
67

In a cuboid of dimension $$2 \mathrm{~L} \times 2 \mathrm{~L} \times \mathrm{L}$$, a charge $$q$$ is placed at the center of the surface '$$\mathrm{S}$$' having area of $$4 \mathrm{~L}^{2}$$. The flux through the opposite surface to '$$\mathrm{S}$$' is given by

JEE Main 2023 (Online) 29th January Morning Shift
68

A point charge of 10 $$\mu$$C is placed at the origin. At what location on the X-axis should a point charge of 40 $$\mu$$C be placed so that the net electric field is zero at $$x=2$$cm on the X-axis?

JEE Main 2023 (Online) 25th January Evening Shift
69

The electric potential at the centre of two concentric half rings of radii R$$_1$$ and R$$_2$$, having same linear charge density $$\lambda$$ is :

JEE Main 2023 (Online) 24th January Evening Shift Physics - Electrostatics Question 88 English

JEE Main 2023 (Online) 24th January Evening Shift
70

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 2023 (Online) 24th January Morning Shift
71

Two identical metallic spheres $$\mathrm{A}$$ and $$\mathrm{B}$$ when placed at certain distance in air repel each other with a force of $$\mathrm{F}$$. Another identical uncharged sphere $$\mathrm{C}$$ is first placed in contact with $$\mathrm{A}$$ and then in contact with $$\mathrm{B}$$ and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be:

JEE Main 2022 (Online) 29th July Evening Shift
72

A spherically symmetric charge distribution is considered with charge density varying as

$$\rho(r)= \begin{cases}\rho_{0}\left(\frac{3}{4}-\frac{r}{R}\right) & \text { for } r \leq R \\ \text { zero } & \text { for } r>R\end{cases}$$

Where, $$r(r < R)$$ is the distance from the centre O (as shown in figure). The electric field at point P will be:

JEE Main 2022 (Online) 29th July Morning Shift Physics - Electrostatics Question 106 English

JEE Main 2022 (Online) 29th July Morning Shift
73

Given below are two statements.

Statement I : Electric potential is constant within and at the surface of each conductor.

Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.

In the light of the above statements, choose the most appropriate answer from the options given below.

JEE Main 2022 (Online) 29th July Morning Shift
74

A uniform electric field $$\mathrm{E}=(8 \mathrm{~m} / \mathrm{e}) \,\mathrm{V} / \mathrm{m}$$ is created between two parallel plates of length $$1 \mathrm{~m}$$ as shown in figure, (where $$\mathrm{m}=$$ mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of $$2 \mathrm{~m} / \mathrm{s}$$. The angle of the deviation $$(\theta)$$ of the path of the electron as it comes out of the field will be _________.

JEE Main 2022 (Online) 28th July Evening Shift Physics - Electrostatics Question 109 English

JEE Main 2022 (Online) 28th July Evening Shift
75

A charge of $$4 \,\mu \mathrm{C}$$ is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be :

JEE Main 2022 (Online) 27th July Evening Shift
76

Two identical positive charges $$Q$$ each are fixed at a distance of '2a' apart from each other. Another point charge $$q_{0}$$ with mass 'm' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $$\mathrm{q}_{0}$$ executes $$\mathrm{SHM}$$. The time period of oscillation of charge $$\mathrm{q}_{0}$$ will be :

JEE Main 2022 (Online) 27th July Morning Shift
77

Two uniformly charged spherical conductors $$A$$ and $$B$$ of radii $$5 \mathrm{~mm}$$ and $$10 \mathrm{~mm}$$ are separated by a distance of $$2 \mathrm{~cm}$$. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere $$A$$ and $$B$$ will be :

JEE Main 2022 (Online) 26th July Evening Shift
78

Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from mid-point on the perpendicular bisector. The value of x at which charge q will experience the maximum Coulomb's force is :

JEE Main 2022 (Online) 29th June Evening Shift
79

If the electric potential at any point (x, y, z) m in space is given by V = 3x2 volt. The electric field at the point (1, 0, 3) m will be :

JEE Main 2022 (Online) 29th June Evening Shift
80

A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength 1 $$\times$$ 105 NC$$-$$1. If the charge on the particle is 40 $$\mu$$C and the initial velocity is 200 ms$$-$$1, how much distance it will travel before coming to the rest momentarily :

JEE Main 2022 (Online) 29th June Morning Shift
81

Two point charges A and B of magnitude +8 $$\times$$ 10$$-$$6 C and $$-$$8 $$\times$$ 10$$-$$6 C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4 $$\times$$ 104 NC$$-$$1. The distance 'd' between the point charges A and B is :

JEE Main 2022 (Online) 28th June Evening Shift
82

Given below are two statements :

Statement I : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive.

Statement II : An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero.

Choose the correct answer from the options given below :

JEE Main 2022 (Online) 28th June Morning Shift
83

The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of side 'a' as shown in figure. The magnitude of electric field (E) at the corner D of the square, is :

JEE Main 2022 (Online) 28th June Morning Shift Physics - Electrostatics Question 126 English

JEE Main 2022 (Online) 28th June Morning Shift
84

If a charge q is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be :

JEE Main 2022 (Online) 27th June Evening Shift Physics - Electrostatics Question 124 English

JEE Main 2022 (Online) 27th June Evening Shift
85

Three identical charged balls each of charge 2 C are suspended from a common point P by silk threads of 2 m each (as shown in figure). They form an equilateral triangle of side 1m.

The ratio of net force on a charged ball to the force between any two charged balls will be :

JEE Main 2022 (Online) 27th June Evening Shift Physics - Electrostatics Question 125 English

JEE Main 2022 (Online) 27th June Evening Shift
86

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

JEE Main 2022 (Online) 26th June Evening Shift
87

Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R).

Assertion (A) : Non-polar materials do not have any permanent dipole moment.

Reason (R) : When a non-polar material is placed in an electric field, the centre of the positive charge distribution of it's individual atom or molecule coincides with the centre of the negative charge distribution.

In the light of above statements, choose the most appropriate answer from the options given below.

JEE Main 2022 (Online) 26th June Morning Shift
88

In the figure, a very large plane sheet of positive charge is shown. P1 and P2 are two points at distance l and 2l from the charge distribution. If $$\sigma$$ is the surface charge density, then the magnitude of electric fields E1 and E2 at P1 and P2 respectively are :

JEE Main 2022 (Online) 25th June Morning Shift Physics - Electrostatics Question 120 English

JEE Main 2022 (Online) 25th June Morning Shift
89

Two identical charged particles each having a mass 10 g and charge 2.0 $$\times$$ 10$$-$$7C are placed on a horizontal table with a separation of L between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is 0.25, find the value of L. [Use g = 10 ms$$-$$2]

JEE Main 2022 (Online) 24th June Evening Shift
90

A long cylindrical volume contains a uniformly distributed charge of density $$\rho$$. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :

JEE Main 2022 (Online) 24th June Evening Shift
91

A vertical electric field of magnitude 4.9 $$\times$$ 105 N/C just prevents a water droplet of a mass 0.1 g from falling. The value of charge on the droplet will be :

(Given : g = 9.8 m/s2)

JEE Main 2022 (Online) 24th June Morning Shift
92
A cube is placed inside an electric field, $$\overrightarrow E = 150{y^2}\widehat j$$. The side of the cube is 0.5 m and is placed in the field as shown in the given figure. The charge inside the cube is :

JEE Main 2021 (Online) 1st September Evening Shift Physics - Electrostatics Question 132 English
JEE Main 2021 (Online) 1st September Evening Shift
93
Choose the incorrect statement :

(1) The electric lines of force entering into a Gaussian surface provide negative flux.

(2) A charge 'q' is placed at the centre of a cube. The flux through all the faces will be the same.

(3) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero.

(4) 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
JEE Main 2021 (Online) 31st August Evening Shift
94
Two particles A and B having charges 20$$\mu$$C and $$-$$5$$\mu$$C respectively are held fixed with a separation of 5 cm. At what position a third charged particle should be placed so that it does not experience a net electric force?

JEE Main 2021 (Online) 31st August Morning Shift Physics - Electrostatics Question 134 English
JEE Main 2021 (Online) 31st August Morning Shift
95
Figure shows a rod AB, which is bent in a 120$$^\circ$$ circular arc of radius R. A charge ($$-$$Q) is uniformly distributed over rod AB. What is the electric field $$\overrightarrow E $$ at the centre of curvature O ?

JEE Main 2021 (Online) 27th August Evening Shift Physics - Electrostatics Question 135 English
JEE Main 2021 (Online) 27th August Evening Shift
96
A uniformly charged disc of radius R having surface charge density $$\sigma$$ is placed in the xy plane with its center at the origin. Find the electric field intensity along the z-axis at a distance Z from origin :-
JEE Main 2021 (Online) 27th August Morning Shift
97
The two thin coaxial rings, each of radius 'a' and having charges +Q and $$-$$Q respectively are separated by a distance of 's'. The potential difference between the centres of the two rings is :
JEE Main 2021 (Online) 26th August Evening Shift
98
A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius b as shown in the figure. The approximate variation electric field $$\overrightarrow E $$ as a function of distance r from centre O is given by

JEE Main 2021 (Online) 26th August Morning Shift Physics - Electrostatics Question 138 English
JEE Main 2021 (Online) 26th August Morning Shift
99
What will be the magnitude of electric field at point O as shown in the figure? Each side of the figure is l and perpendicular to each other?

JEE Main 2021 (Online) 27th July Evening Shift Physics - Electrostatics Question 139 English
JEE Main 2021 (Online) 27th July Evening Shift
100
Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle '$$\theta$$' with the vertical?
JEE Main 2021 (Online) 27th July Morning Shift
101
Two ideal electric dipoles A and B, having their dipole moment p1 and p2 respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle of 37$$^\circ$$ with the axis. The ratio of the dipole moment of A and B, $${{{p_1}} \over {{p_2}}}$$ is : (take $$\sin 37^\circ = {3 \over 5}$$)

JEE Main 2021 (Online) 25th July Evening Shift Physics - Electrostatics Question 141 English
JEE Main 2021 (Online) 25th July Evening Shift
102
An electric dipole is placed on x-axis in proximity to a line charge of linear charge density 3.0 $$\times$$ 10$$-$$6 C/m. Line charge is placed on z-axis and positive and negative charge of dipole is at a distance of 10 mm and 12 mm from the origin respectively. If total force of 4N is exerted on the dipole, find out the amount of positive or negative charge of the dipole.
JEE Main 2021 (Online) 22th July Evening Shift
103
A certain charge Q is divided into two parts q and (Q $$-$$ q). How should the charges Q and q be divided so that q and (Q $$-$$ q) placed at a certain distance apart experience maximum electrostatic repulsion?
JEE Main 2021 (Online) 20th July Morning Shift
104
An oil drop of radius 2 mm with a density 3g cm$$-$$3 is held stationary under a constant electric field 3.55 $$\times$$ 105 V m$$-$$1 in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? (consider g = 9.81 m/s2)
JEE Main 2021 (Online) 18th March Morning Shift
105
Find out the surface charge density at the intersection of point x = 3 m plane and x-axis, in the region of uniform line charge of 8 nC/m lying along the z-axis in free space.
JEE Main 2021 (Online) 16th March Evening Shift
106
Given below are two statements:

Statement I : An electric dipole is placed at the center of a hollow sphere. The flux of the electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.

Statement II : If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius r (< R) is zero but the electric flux passing through this closed spherical surface of radius r is not zero..

In the light of the above statements, choose the correct answer from the options given below :
JEE Main 2021 (Online) 26th February Evening Shift
107
An inclined plane making an angle of 30$$^\circ$$ with the horizontal is placed in a uniform horizontal electric field $$200{N \over C}$$ as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a height of 1 m. If the coefficient of friction is 0.2, find the time taken by the body to reach the bottom.

[g = 9.8 m/s2; $$\sin 30^\circ = {1 \over 2}$$; $$\cos 30^\circ = {{\sqrt 3 } \over 2}$$]

JEE Main 2021 (Online) 26th February Evening Shift Physics - Electrostatics Question 152 English
JEE Main 2021 (Online) 26th February Evening Shift
108
Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point P from the centre of the rod is a = $${{\sqrt 3 } \over 2}L$$.

JEE Main 2021 (Online) 26th February Morning Shift Physics - Electrostatics Question 154 English
JEE Main 2021 (Online) 26th February Morning Shift
109
A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field $$\overrightarrow E $$ through the shaded area is :

JEE Main 2021 (Online) 25th February Evening Shift Physics - Electrostatics Question 156 English
JEE Main 2021 (Online) 25th February Evening Shift
110
Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x << d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : (m = mass of charged particle)
JEE Main 2021 (Online) 24th February Evening Shift
111
A cube of side 'a' has point charges +Q located at each of its vertices except at the origin where the charge is $$-$$Q. The electric field at the centre of cube is :

JEE Main 2021 (Online) 24th February Morning Shift Physics - Electrostatics Question 162 English
JEE Main 2021 (Online) 24th February Morning Shift
112
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 centre of the shell?
JEE Main 2020 (Online) 6th September Evening Slot
113
Two identical electric point dipoles have dipole moments $${\overrightarrow p _1} = p\widehat i$$ and $${\overrightarrow p _2} = - p\widehat i$$ and are held on the x axis at distance '$$a$$' from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is 'm', their speed when they are infinitely far apart is :
JEE Main 2020 (Online) 6th September Evening Slot
114
Charges Q1 and Q2 are at points A and B of a right angle triangle OAB (see figure). The resultant electric field at point O is perpendicular to the hypotenuse, then
$${{{Q_1}} \over {{Q_2}}}$$ is proportional to : JEE Main 2020 (Online) 6th September Morning Slot Physics - Electrostatics Question 165 English
JEE Main 2020 (Online) 6th September Morning Slot
115
Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+q) each, while 2, 4, 6, 8, 10 have charge (–q) each. The potential V and the electric field E at the centre of the circle are respectively.
(Take V = 0 at infinity)
JEE Main 2020 (Online) 5th September Evening Slot
116
A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquires a speed v when it has fallen through a vertical height y (see figure), then :
(assume the remaining portion to be spherical). JEE Main 2020 (Online) 5th September Morning Slot Physics - Electrostatics Question 167 English
JEE Main 2020 (Online) 5th September Morning Slot
117
A particle of charge q and mass m is subjected to an electric field
E = E0 (1 – $$a$$x2) in the x-direction, where $$a$$ and E0 are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :
JEE Main 2020 (Online) 4th September Evening Slot
118
A two point charges 4q and -q are fixed on the x-axis at x = $$ - {d \over 2}$$ and x = $${d \over 2}$$ respectively. If a third point charge 'q' is taken from the origin to x = d along the semicircle as shown in the figure, the energy of the charge will : JEE Main 2020 (Online) 4th September Morning Slot Physics - Electrostatics Question 174 English
JEE Main 2020 (Online) 4th September Morning Slot
119
Two charged thin infinite plane sheets of
uniform surface charge density $${\sigma _ + }$$ and $${\sigma _ - }$$,
where |$${\sigma _ + }$$| > |$${\sigma _ - }$$|, intersect at right angle.
Which of the following best represents the
electric field lines for this system :
JEE Main 2020 (Online) 4th September Morning Slot
120
Concentric metallic hollow spheres of radii R and 4R hold charges Q1 and Q2 respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V(R) – V(4R) is :
JEE Main 2020 (Online) 3rd September Evening Slot
121
Two isolated conducting spheres S1 and S2 of radius $${2 \over 3}R$$ and $${1 \over 3}R$$ have 12 $$\mu $$C and –3 $$\mu $$C charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done the charges on S1 and S2 are respectively :
JEE Main 2020 (Online) 3rd September Morning Slot
122
A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R > r). If the surface charge densities on the two shells are equal, the electric potential at the common centre is : JEE Main 2020 (Online) 2nd September Evening Slot Physics - Electrostatics Question 171 English
JEE Main 2020 (Online) 2nd September Evening Slot
123
A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass?
(Curves are drawn schematically and are not to scale). JEE Main 2020 (Online) 2nd September Evening Slot Physics - Electrostatics Question 172 English
JEE Main 2020 (Online) 2nd September Evening Slot
124
A charged particle (mass m and charge q)
moves along X-axis with velocity V0. When it
passes through the origin it enters a region having uniform electric field
$$\overrightarrow E = - E\widehat j$$ which extends upto x = d.
Equation of path of electron in the region x > d is JEE Main 2020 (Online) 2nd September Morning Slot Physics - Electrostatics Question 173 English
JEE Main 2020 (Online) 2nd September Morning Slot
125
Consider a sphere of radius R which carries a uniform charge density $$\rho $$. If a sphere of radius $${{R \over 2}}$$ is carved out of it, as shown, the ratio $${{\left| {\overrightarrow {{E_A}} } \right|} \over {\left| {\overrightarrow {{E_B}} } \right|}}$$ of magnitude of electric field $${\overrightarrow {{E_A}} }$$ and $${\overrightarrow {{E_B}} }$$, respectively, at points A and B due to the remaining portion is : JEE Main 2020 (Online) 9th January Morning Slot Physics - Electrostatics Question 178 English
JEE Main 2020 (Online) 9th January Morning Slot
126
An electric dipole of moment
$$\overrightarrow p = \left( { - \widehat i - 3\widehat j + 2\widehat k} \right) \times {10^{ - 29}} $$ C.m is
at the origin (0, 0, 0). The electric field due to this dipole at
$$\overrightarrow r = + \widehat i + 3\widehat j + 5\widehat k$$ (note that $$\overrightarrow r .\overrightarrow p = 0$$ ) is parallel to :
JEE Main 2020 (Online) 9th January Morning Slot
127
A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is correctly given by (graphs are schematic and not drawn to scale)
JEE Main 2020 (Online) 8th January Evening Slot
128
Consider two charged metallic spheres S1 and S2 of radii R1 and R2, respectively. The electric fields E1 (on S1) and E2 (on S2) on their surfaces are such that E1/E2 = R1/R2. Then the ratio V1 (on S1) / V2 (on S2) of the electrostatic potentials on each sphere is :
JEE Main 2020 (Online) 8th January Evening Slot
129
In finding the electric field using Gauss Law the formula $$\left| {\overrightarrow E } \right| = {{{q_{enc}}} \over {{\varepsilon _0}\left| A \right|}}$$ is applicable. In the formula $${{\varepsilon _0}}$$ is permittivity of free space, A is the area of Gaussian surface and qenc is charge enclosed by the Gaussian surface. The equation can be used in which of the following situation?
JEE Main 2020 (Online) 8th January Morning Slot
130
Three charged particle A, B and C with charges –4q, 2q and –2q are present on the circumference of a circle of radius d. the charged particles A, C and centre O of the circle formed an equilateral triangle as shown in figure. Electric field at O along x-direction is : JEE Main 2020 (Online) 8th January Morning Slot Physics - Electrostatics Question 181 English
JEE Main 2020 (Online) 8th January Morning Slot
131
Two infinite planes each with uniform surface charge density to are kept in such a way that the angle between them is 30o. The electric field in the region shown between them is given by : JEE Main 2020 (Online) 7th January Morning Slot Physics - Electrostatics Question 183 English
JEE Main 2020 (Online) 7th January Morning Slot
132
Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by $$\rho $$(r) = kr, where r is the distance from the centre. Two charges A and B, of –Q each, are placed on diametrically opposite points, at equal distance, $$a$$ from the centre. If A and B do not experience any force, then :
JEE Main 2019 (Online) 12th April Evening Slot
133
A point dipole $$\overrightarrow p = - {p_0}\widehat x$$ is kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively: (Take V= 0 at infinity)
JEE Main 2019 (Online) 12th April Morning Slot
134
Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre is a dipole $$\overrightarrow P $$ as shown. In this case : JEE Main 2019 (Online) 12th April Morning Slot Physics - Electrostatics Question 186 English
JEE Main 2019 (Online) 12th April Morning Slot
135
In free space, a particle A of charge 1$$\mu $$C is held fixed at a point P. Another particle B of the same charge and mass 4$$\mu $$g is kept at a distance of 1 mm from P. If B is released, then its velocity at a distance of 9 mm from P is : $$\left[ {Take\,{1 \over {4\pi { \in _0}}} = 9 \times {{10}^9}N{m^2}{C^{ - 2}}} \right]$$
JEE Main 2019 (Online) 10th April Evening Slot
136
A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centred at origin. A point charge q is moving towards the ring along the z-axis and has speed u at z = 4a. The minimum value of u such that it crosses the origin is :
JEE Main 2019 (Online) 10th April Morning Slot
137
Four point charges –q, +q, +q and –q are placed on y-axis at y = –2d, y = –d, y = +d and y = +2d, respectively. The magnitude of the electric field E at a point on the x-axis at x = D, with D >> d, will behave as :-
JEE Main 2019 (Online) 9th April Evening Slot
138
A system of three charges are placed as shown in the figure :

JEE Main 2019 (Online) 9th April Morning Slot Physics - Electrostatics Question 190 English If D >> d, the potential energy of the system is best given by :
JEE Main 2019 (Online) 9th April Morning Slot
139
A positive point charge is released from rest at a distance r0 from a positive line charge with uniform density. The speed (v) of the point charge, as a function of instantaneous distance r from line charge, is proportional to :- JEE Main 2019 (Online) 8th April Evening Slot Physics - Electrostatics Question 192 English
JEE Main 2019 (Online) 8th April Evening Slot
140
The electric field in a region is given by $$\mathop E\limits^ \to = \left( {Ax + B} \right)\mathop i\limits^ \wedge $$ , where E is in NC–1 and x is in metres. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is V1 and that at x = –5 is V2, then V1 – V2 is :-
JEE Main 2019 (Online) 8th April Evening Slot
141
A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of –4 Q, the new potential difference between the same two surfaces is :
JEE Main 2019 (Online) 8th April Morning Slot
142
The bob of a simple pendulum has mass 2g and a charge of 5.0 μC. It is at rest in a uniform horizontal electric field of intensity 2000 V/m. At equilibrium, the angle that the pendulum makes with the vertical is : (take g = 10 m/s2)
JEE Main 2019 (Online) 8th April Morning Slot
143
Determine the electric dipole moment of the system of the three charges, placed on the vertices of an equilateral triangle, as shown in the figure :

JEE Main 2019 (Online) 12th January Morning Slot Physics - Electrostatics Question 196 English
JEE Main 2019 (Online) 12th January Morning Slot
144
There is a uniform spherically symmetric surface charge density at a distance R0 from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V (R(t)) of the distribution as a function of its instantaneous radius R (t) is :
JEE Main 2019 (Online) 12th January Morning Slot
145
An electric field of 1000 V/m is applied to an electric dipole at angle of 45o. The value of electric dipole moment is 10–29 C.m. What is the potential energy of the electric dipole?
JEE Main 2019 (Online) 11th January Evening Slot
146
Three charges Q, + q and + q are placed at the vertices of a right-angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of Q is :

JEE Main 2019 (Online) 11th January Morning Slot Physics - Electrostatics Question 199 English
JEE Main 2019 (Online) 11th January Morning Slot
147
The given graph shows variation (with distance r form centre) of :

JEE Main 2019 (Online) 11th January Morning Slot Physics - Electrostatics Question 198 English
JEE Main 2019 (Online) 11th January Morning Slot
148
Four equal point charges Q each are placed in the xy plane at (0, 2), (4, 2), (4, –2) and (0, –2). The work required to put a fifth charge Q at the origin of the coordinate system will be -
JEE Main 2019 (Online) 10th January Evening Slot
149
Charges –q and +q located at A and B, respectively, constitude an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP = y and y >> 2a. The charge Q experiences an electrostatic force F. If Q is now moved along the equatorial line to P' such that OP' = $$\left( {{y \over 3}} \right)$$, the force on Q will be close to - $$\left( {{y \over 3} > > 2a} \right)$$

JEE Main 2019 (Online) 10th January Evening Slot Physics - Electrostatics Question 200 English
JEE Main 2019 (Online) 10th January Evening Slot
150
A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be -
JEE Main 2019 (Online) 10th January Morning Slot
151
Two electric dipoles, A, B with respective dipole moments $${\overrightarrow d _A} = - 4qai$$ and $${\overrightarrow d _B} = - 2qai$$ are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is -

JEE Main 2019 (Online) 10th January Morning Slot Physics - Electrostatics Question 202 English
JEE Main 2019 (Online) 10th January Morning Slot
152
Two point charges q1$$\left( {\sqrt {10} \mu C} \right)$$ and q2($$-$$ 25 $$\mu $$C) are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y-axis is,
[take $${1 \over {4\pi { \in _0}}}$$ = 9 $$ \times $$ 109 Nm2C$$-$$2]
JEE Main 2019 (Online) 9th January Evening Slot
153
Charge is distributed within a sphere of radius R with a volume charge density $$\rho \left( r \right) = {A \over {{r^2}}}{e^{ - {{2r} \over s}}},$$ where A and a are constants. If Q is the total charge of this charge distribution, the radius R is :
JEE Main 2019 (Online) 9th January Evening Slot
154
Three charges + Q, q, + Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis. If the net force experienced by + Q, placed at x = 0, is zero, then value of q is :
JEE Main 2019 (Online) 9th January Morning Slot
155
For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its center. Then value of h is :
JEE Main 2019 (Online) 9th January Morning Slot
156
Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameters, and the force between theis F. A third identical conducting sphere, C, is uncharged. Sphere C is first touhed to A, then to B, and then removed. As a result, the force between A and B would be equal to :
JEE Main 2018 (Online) 16th April Morning Slot
157
Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities $$ + \sigma $$, $$ - \sigma $$ and $$ + \sigma $$ respectively. The potential of shell B is :
JEE Main 2018 (Offline)
158
A solid ball of radius R has a charge density $$\rho $$
given by $$\rho $$ = $$\rho $$o (1 $$-$$ $${\raise0.5ex\hbox{$\scriptstyle r$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle R$}}$$) for 0 $$ \le $$ r $$ \le $$ R. The electric field outside the ball is :
JEE Main 2018 (Online) 15th April Evening Slot
159
A charge $$Q$$ is placed at a distance $$a/2$$ above the center of the square surface of edge a as shown in the figure.

JEE Main 2018 (Online) 15th April Morning Slot Physics - Electrostatics Question 214 English
The electric flux through the square surface is
JEE Main 2018 (Online) 15th April Morning Slot
160
A body of mass $$M$$ and charge $$q$$ is connected to spring of spring constant $$k.$$ It is oscillating along $$x$$-direction about its equilibrium position, taken to be at $$x=0,$$ with an amplitude $$A$$. An electric field $$E$$ is applied along the $$x$$-direction. Which of the following statements is correct ?
JEE Main 2018 (Online) 15th April Morning Slot
161
Four closed surfaces and corresponding charge distributions are shown below.

JEE Main 2017 (Online) 9th April Morning Slot Physics - Electrostatics Question 210 English

Let the respective electric fluxes through the surfaces be $${\Phi _1},$$ $${\Phi _2},$$ $${\Phi _3}$$ and $${\Phi _4}$$. Then :
JEE Main 2017 (Online) 9th April Morning Slot
162
There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $$P,$$ in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of 60o with the direction of the field ?
JEE Main 2017 (Online) 8th April Morning Slot
163
An electric dipole has a fixed dipole moment $$\overrightarrow p $$, which makes angle $$\theta$$ with respect to x-axis. When subjected to an electric field $$\mathop {{E_1}}\limits^ \to = E\widehat i$$ , it experiences a torque $$\overrightarrow {{T_1}} = \tau \widehat k$$ . When subjected to another electric field $$\mathop {{E_2}}\limits^ \to = \sqrt 3 {E_1}\widehat j$$ it experiences a torque $$\mathop {{T_2}}\limits^ \to = \mathop { - {T_1}}\limits^ \to $$ . The angle $$\theta$$ is:
JEE Main 2017 (Offline)
164
Within a spherical charge distribution of charge density $$\rho $$(r), N equipotential surfaces of potential V0, V0 + $$\Delta $$V, V0 + 2$$\Delta $$V, .......... V0 + N$$\Delta $$V ($$\Delta $$ V > 0), are drawn and have increasing radii r0, r1, r2,..........rN, respectively. If the difference in the radii of the surfaces is constant for all values of V0 and $$\Delta $$V then :
JEE Main 2016 (Online) 10th April Morning Slot
165
The potential (in volts) of a charge distribution is given by.

V(z) = 30 $$-$$ 5x2 for $$\left| z \right|$$ $$ \le $$ 1 m.
V(z) = 35 $$-$$ 10 $$\left| z \right|$$ for $$\left| z \right|$$ $$ \ge $$1 m.

V(z) does not depend on x and y. If this potential is generated by a constant charge per unit volume $${\rho _0}$$ (in units of $${\varepsilon _0}$$) which is spread over a certain region, then choose the correct statement.
JEE Main 2016 (Online) 9th April Morning Slot
166
The region between two concentric spheres of radii $$'a'$$ and $$'b',$$ respectively (see figure), have volume charge density $$\rho = {A \over r},$$ where $$A$$ is a constant and $$r$$ is the distance from the center. A such that the electric field in the region between the spheres will be constant, is :

JEE Main 2016 (Offline) Physics - Electrostatics Question 218 English
JEE Main 2016 (Offline)
167
A long cylindrical shell carries positives surfaces change $$\sigma $$ in the upper half and negative surface charge - $$\sigma $$ in the lower half. The electric field lines around the cylinder will look like figure given in :
(figures are schematic and not drawn to scale)
JEE Main 2015 (Offline)
168
Assume that an electric field $$\overrightarrow E = 30{x^2}\widehat i$$ exists in space. Then the potential difference $${V_A} - {V_O},$$ where $${V_O}$$ is the potential at the origin and $${V_A}$$ the potential at $$x=2$$ $$m$$ is :
JEE Main 2014 (Offline)
169
Two charges, each equals to $$q,$$ are kept at $$x=-a$$ and $$x=a$$ on the $$x$$-axis. A particle of mass $$m$$ and charge $${q_0} = {q \over 2}$$ is placed at the origin. If charge $${q_0}$$ is given a small displacement $$\left( {y < < a} \right)$$ along the $$y$$-axis, the net force acting on the particle is proportional to
JEE Main 2013 (Offline)
170
A charge $$Q$$ is uniformly distributed over a long rod $$AB$$ of length $$L$$ as shown in the figure. The electric potential at the point $$O$$ lying at distance $$L$$ from the end $$A$$ is JEE Main 2013 (Offline) Physics - Electrostatics Question 222 English
JEE Main 2013 (Offline)
171
This question has statement- $$1$$ and statement- $$2.$$ Of the four choices given after the statements, choose the one that best describe the two statements.
An insulating solid sphere of radius $$R$$ has a uniformly positive charge density $$\rho $$. As a result of this uniform charge distribution there is a finite value of electric potential at the center of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinite is zero.

Statement- $$1:$$ When a charge $$q$$ is take from the centre of the surface of the sphere its potential energy changes by $${{q\rho } \over {3{\varepsilon _0}}}$$
Statement- $$2:$$ The electric field at a distance $$r\left( {r < R} \right)$$ from the center of the sphere is $${{\rho r} \over {3{\varepsilon _0}}}.$$

AIEEE 2012
172
In a uniformly charged sphere of total charge $$Q$$ and radius $$R,$$ the electric field $$E$$ is plotted as function of distance from the center. The graph which would correspond to the above will be:
AIEEE 2012
173
Two identical charged spheres suspended from a common point by two massless strings of length $$l$$ are initially a distance $$d\left( {d < < 1} \right)$$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result charges approach each other with a velocity $$v$$. Then as a function of distance $$x$$ between them,
AIEEE 2011
174
The electrostatic potential inside a charged spherical ball is given by $$\phi = a{r^2} + b$$ where $$r$$ is the distance from the center and $$a,b$$ are constants. Then the charge density inside the ball is:
AIEEE 2011
175
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $${30^ \circ }$$ with each other. When suspended in a liquid of density $$0.8g$$ $$c{m^{ - 3}},$$ the angle remains the same. If density of the material of the sphere is $$1.6$$ $$g$$ $$c{m^{ - 3}},$$ the dielectric constant of the liquid is
AIEEE 2010
176
Let there be a spherically symmetric charge distribution with charge density varying as $$\rho \left( r \right) = {\rho _0}\left( {{5 \over 4} - {r \over R}} \right)$$ upto $$r=R,$$ and $$\rho \left( r \right) = 0$$ for $$r>R,$$ where $$r$$ is the distance from the erigin. The electric field at a distance $$r\left( {r < R} \right)$$ from the origin is given by
AIEEE 2010
177
A thin semi-circular ring of radius $$r$$ has a positive charges $$q$$ distributed uniformly over it. The net field $$\overrightarrow E $$ at the center $$O$$ is AIEEE 2010 Physics - Electrostatics Question 229 English
AIEEE 2010
178
A charge $$Q$$ is placed at each of the opposite corners of a square. A charge $$q$$ is placed at each of the other two corners. If the net electrical force on $$Q$$ is zero, then $$Q/q$$ equals:
AIEEE 2009
179
Let $$P\left( r \right) = {Q \over {\pi {R^4}}}r$$ be the change density distribution for a solid sphere of radius $$R$$ and total charge $$Q$$. For a point $$'p'$$ inside the sphere at distance $${r_1}$$ from the center of the sphere, the magnitude of electric field is :
AIEEE 2009
180
Two points $$P$$ and $$Q$$ are maintained at the potentials of $$10$$ $$V$$ and $$-4$$ $$V$$, respectively. The work done in moving $$100$$ electrons from $$P$$ to $$Q$$ is :
AIEEE 2009
181
(This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.)

Statement-1 : For a charged particle moving from point $$P$$ to point $$Q$$, the net work done by an electrostatic field on the particle is independent of the path connecting point $$P$$ to point $$Q.$$
Statement-2 : The net work done by a conservative force on an object moving along a closed loop is zero.

AIEEE 2009
182
A thin spherical shell of radius $$R$$ has charge $$Q$$ spread uniformly over its surface. Which of the following graphs most closely represents the electric field $$E(r)$$ produced by the shell in the range $$0 \le r < \infty ,$$ where $$r$$ is the distance from the center of the shell?
AIEEE 2008
183
An electric charge $${10^{ - 3}}\,\,\mu \,C$$ is placed at the origin $$(0,0)$$ of $$X-Y$$ co-ordinate system. Two points $$A$$ and $$B$$ are situated at $$\left( {\sqrt 2 ,\sqrt 2 } \right)$$ and $$\left( {2,0} \right)$$ respectively. The potential difference between the points $$A$$ and $$B$$ will be
AIEEE 2007
184
Charges are placed on the vertices of a square as shown. Let $$\overrightarrow E $$ be the electric field and $$V$$ the potential at the center. If the charges on $$A$$ and $$B$$ are interchanged with those on $$D$$ and $$C$$ respectively, then AIEEE 2007 Physics - Electrostatics Question 236 English
AIEEE 2007
185
The potential at a point $$x$$ (measured in $$\mu \,m$$) due to some charges situated on the $$x$$-axis is given by $$V\left( x \right) = 20/\left( {{x^2} - 4} \right)$$ volt
The electric field $$E$$ at $$x = 4\,\mu \,m$$ is given by
AIEEE 2007
186
An electric dipole is placed at an angle of $${30^ \circ }$$ to a non-uniform electric field. The dipole will experience
AIEEE 2006
187
Two spherical conductors $$A$$ and $$B$$ of radii $$1$$ $$mm$$ and $$2$$ $$mm$$ are separated by a distance of $$5$$ $$cm$$ and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres $$A$$ and $$B$$ is
AIEEE 2006
188
Two insulating plates are both uniformly charged in such a way that the potential difference between them is $${V_2} - {V_1} = 20\,V.$$ (i.e., plate $$2$$ is at a higher potential). The plates are separated by $$d=0.1$$ $$m$$ and can be treated as infinitely large. An electron is released from rest on the inner surface of plate $$1.$$ What is its speed when it hits plate $$2$$?
$$\left( {e = 1.6 \times {{10}^{ - 19}}\,C,\,\,{m_e} = 9.11 \times {{10}^{ - 31}}\,kg} \right)$$ AIEEE 2006 Physics - Electrostatics Question 237 English
AIEEE 2006
189
Two thin wire rings each having a radius $$R$$ are placed at a distance $$d$$ apart with their axes coinciding. The charges on the two rings are $$+q$$ and $$-q.$$ The potential difference between the centres of the two rings is
AIEEE 2005
190
A charged ball $$B$$ hangs from a silk thread $$S,$$ which makes angle $$\theta $$ with a large charged conducting sheet $$P,$$ as shown in the figure. The surface charge density $$\sigma $$ of the sheet is proportional to AIEEE 2005 Physics - Electrostatics Question 241 Englishf
AIEEE 2005
191
Two point charges $$+8q$$ and $$-2q$$ are located at $$x=0$$ and $$x=L$$ respectively. The location of a point on the $$x$$ axis at which the net electric field due to these two point charges is zero is
AIEEE 2005
192
Two spherical conductors $$B$$ and $$C$$ having equal radii and carrying equal charges on them repel each other with a force $$F$$ when kept apart at some distance. A third spherical conductor having same radius as that $$B$$ but uncharged is brought in contact with $$B,$$ then brought in correct with $$C$$ and finally removed away from both. The new force of repulsion between $$B$$ and $$C$$ is
AIEEE 2004
193
A charge particle $$'q'$$ is shot towards another charged particle $$'Q'$$ which is fixed, with a speed $$'v'$$. It approaches $$'Q'$$ upto a closest distance $$r$$ and then returns. If $$q$$ were given a speed of $$'2v'$$ the closest distances of approaches would be
AIEEE 2004
194
Four charges equal to -$$Q$$ are placed at the four corners of a square and a charge $$q$$ is at its center. If the system is in equilibrium the value of $$q$$ is
AIEEE 2004
195
A charged oil drop is suspended in a uniform field of $$3 \times {10^4}$$ $$v/m$$ so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge $$ = 9.9 \times {10^{ - 15}}\,\,kg$$ and $$g = 10\,m/{s^2}$$)
AIEEE 2004
196
If the electric flux entering and leaving an enclosed surface respectively is $${\phi _1}$$ and $${\phi _2},$$ the electric charge inside the surface will be
AIEEE 2003
197
A thin spherical conducting shell of radius $$R$$ has a charge $$q.$$ Another charge $$Q$$ is placed at the center of the shell. The electrostatic potential at a point $$P$$ a distance $${R \over 2}$$ from the center of the shell is
AIEEE 2003
198
Three charges $$ - {q_1}, + {q_2}$$ and $$ - {q_3}$$ are placed as shown in the figure. The $$x$$-component of the force on $$ - {q_1}$$ is proportional to AIEEE 2003 Physics - Electrostatics Question 248 English
AIEEE 2003
199
On moving a charge of $$20$$ coulomb by $$2$$ $$cm,$$ $$2$$ $$J$$ of work is done, then the potential differences between the points is
AIEEE 2002
200
A charged particle $$q$$ is placed at the centre $$O$$ of cube of length $$L(ABCDEFGH).$$ Another same charge $$q$$ is placed at a distance $$L$$ from $$O$$. Then the electric flux through $$ABCD$$ is AIEEE 2002 Physics - Electrostatics Question 252 English
AIEEE 2002
201
If a charge $$q$$ is placed at the center of the line joining two equal charges $$Q$$ such that the system is in equilibrium then the value of $$q$$ is
AIEEE 2002

Numerical

1
The electric field in a region is given by $\overrightarrow{\mathrm{E}}=(2 \hat{i}+4 \hat{j}+6 \hat{k}) \times 10^3 \mathrm{~N} / \mathrm{C}$. The flux of the field through a rectangular surface parallel to $x-z$ plane is $6.0 \,\mathrm{Nm}^2 \mathrm{C}^{-1}$. The area of the surface is _____________ $\mathrm{cm}^2$.
JEE Main 2025 (Online) 7th April Evening Shift
2
An electric dipole of dipole moment $6 \times 10^{-6} \mathrm{Cm}$ is placed in uniform electric field of magnitude $10^{6} \mathrm{V} / \mathrm{m}$. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be _______ J.
JEE Main 2025 (Online) 28th January Evening Shift
3

A square loop of sides $a=1 \mathrm{~m}$ is held normally in front of a point charge $\mathrm{q}=1 \mathrm{C}$ at a distance $\frac{\mathrm{a}}{2}$. The flux of the electric field through the shaded region is $\frac{5}{\mathrm{p}} \times \frac{1}{\varepsilon_0} \frac{\mathrm{Nm}^2}{\mathrm{C}}$, where the value of p is ________ .

JEE Main 2025 (Online) 24th January Morning Shift Physics - Electrostatics Question 24 English

JEE Main 2025 (Online) 24th January Morning Shift
4

A positive ion $A$ and a negative ion $B$ has charges $6.67 \times 10^{-19} \mathrm{C}$ and $9.6 \times 10^{-10} \mathrm{C}$, and masses $19.2 \times 10^{-27} \mathrm{~kg}$ and $9 \times 10^{-27} \mathrm{~kg}$ respectively. At an instant, the ions are separated by a certain distance $r$. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is $\mathrm{P} \times 10^{-13}$, where the value of P is _________.

(Take $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-1}$ and universal gravitational constant as $6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}$ )

JEE Main 2025 (Online) 23rd January Morning Shift
5

An electric field $$\vec{E}=(2 x \hat{i}) N C^{-1}$$ exists in space. A cube of side $$2 \mathrm{~m}$$ is placed in the space as per figure given below. The electric flux through the cube is ______ $$\mathrm{Nm}^2 / \mathrm{C}$$.

JEE Main 2024 (Online) 9th April Evening Shift Physics - Electrostatics Question 51 English

JEE Main 2024 (Online) 9th April Evening Shift
6

At the centre of a half ring of radius $$\mathrm{R}=10 \mathrm{~cm}$$ and linear charge density $$4 \mathrm{~nC} \mathrm{~m}^{-1}$$, the potential is $$x \pi \mathrm{V}$$. The value of $$x$$ is _________.

JEE Main 2024 (Online) 9th April Morning Shift
7

If the net electric field at point $$\mathrm{P}$$ along $$\mathrm{Y}$$ axis is zero, then the ratio of $$\left|\frac{q_2}{q_3}\right|$$ is $$\frac{8}{5 \sqrt{x}}$$, where $$x=$$ ________.

JEE Main 2024 (Online) 8th April Evening Shift Physics - Electrostatics Question 46 English

JEE Main 2024 (Online) 8th April Evening Shift
8

An electric field, $$\overrightarrow{\mathrm{E}}=\frac{2 \hat{i}+6 \hat{j}+8 \hat{k}}{\sqrt{6}}$$ passes through the surface of $$4 \mathrm{~m}^2$$ area having unit vector $$\hat{n}=\left(\frac{2 \hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right)$$. The electric flux for that surface is _________ $$\mathrm{Vm}$$.

JEE Main 2024 (Online) 8th April Morning Shift
9

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $$P$$ is $$\frac{x \sigma}{\epsilon_0}$$. The value of $$x$$ is _________ (all quantities are measured in SI units).

JEE Main 2024 (Online) 6th April Morning Shift Physics - Electrostatics Question 38 English

JEE Main 2024 (Online) 6th April Morning Shift
10

The electric field at point $$\mathrm{p}$$ due to an electric dipole is $$\mathrm{E}$$. The electric field at point $$\mathrm{R}$$ on equitorial line will be $$\frac{\mathrm{E}}{x}$$. The value of $$x$$ :

JEE Main 2024 (Online) 5th April Evening Shift Physics - Electrostatics Question 41 English

JEE Main 2024 (Online) 5th April Evening Shift
11

An infinite plane sheet of charge having uniform surface charge density $$+\sigma_{\mathrm{s}} \mathrm{C} / \mathrm{m}^2$$ is placed on $$x$$-$$y$$ plane. Another infinitely long line charge having uniform linear charge density $$+\lambda_e \mathrm{C} / \mathrm{m}$$ is placed at $$z=4 \mathrm{~m}$$ plane and parallel to $$y$$-axis. If the magnitude values $$\left|\sigma_{\mathrm{s}}\right|=2\left|\lambda_{\mathrm{e}}\right|$$ then at point $$(0,0,2)$$, the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $$\pi \sqrt{n}: 1$$. The value of $$n$$ is _________.

JEE Main 2024 (Online) 4th April Morning Shift
12
Suppose a uniformly charged wall provides a uniform electric field of $2 \times 10^4 \mathrm{~N} / \mathrm{C}$ normally. A charged particle of mass $2 \mathrm{~g}$ being suspended through a silk thread of length $20 \mathrm{~cm}$ and remain stayed at a distance of $10 \mathrm{~cm}$ from the wall.

Then the charge on the particle will be $\frac{1}{\sqrt{x}} \mu \mathrm{C}$ where $x=$ ___________ . [use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ]

JEE Main 2024 (Online) 1st February Evening Shift
13
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is $1.5 \mathrm{~g} / \mathrm{cc}$, the dielectric constant of water will be __________.

(Take density of water $=1 \mathrm{~g} / \mathrm{cc}$ )
JEE Main 2024 (Online) 1st February Morning Shift
14

The distance between charges $$+q$$ and $$-q$$ is $$2 l$$ and between $$+2 q$$ and $$-2 q$$ is $$4 l$$. The electrostatic potential at point $$P$$ at a distance $$r$$ from center $$O$$ is $$-\alpha\left[\frac{q l}{r^2}\right] \times 10^9 \mathrm{~V}$$, where the value of $$\alpha$$ is __________. (Use $$\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{~Nm}^2 \mathrm{C}^{-2}$$)

JEE Main 2024 (Online) 31st January Evening Shift Physics - Electrostatics Question 61 English

JEE Main 2024 (Online) 31st January Evening Shift
15

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $$37^{\circ}$$ with each other. When suspended in a liquid of density $$0.7 \mathrm{~g} / \mathrm{cm}^3$$, the angle remains same. If density of material of the sphere is $$1.4 \mathrm{~g} / \mathrm{cm}^3$$, the dielectric constant of the liquid is _______ $$\left(\tan 37^{\circ}=\frac{3}{4}\right)$$

JEE Main 2024 (Online) 30th January Evening Shift
16

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $$\mathrm{S}$$ having surface charge density $$+\sigma$$. The electron at $$t=0$$ is at a distance of $$1 \mathrm{~m}$$ from $$S$$ and has a speed of $$1 \mathrm{~m} / \mathrm{s}$$. The maximum value of $$\sigma$$ if the electron strikes $$S$$ at $$t=1 \mathrm{~s}$$ is $$\alpha\left[\frac{m \epsilon_0}{e}\right] \frac{C}{m^2}$$, the value of $$\alpha$$ is ___________.

JEE Main 2024 (Online) 29th January Morning Shift
17

Two charges of $$-4 \mu \mathrm{C}$$ and $$+4 \mu \mathrm{C}$$ are placed at the points $$\mathrm{A}(1,0,4) \mathrm{m}$$ and $$\mathrm{B}(2,-1,5) \mathrm{m}$$ located in an electric field $$\overrightarrow{\mathrm{E}}=0.20 \hat{i} \mathrm{~V} / \mathrm{cm}$$. The magnitude of the torque acting on the dipole is $$8 \sqrt{\alpha} \times 10^{-5} \mathrm{Nm}$$, where $$\alpha=$$ _________.

JEE Main 2024 (Online) 27th January Evening Shift
18

The electric potential at the surface of an atomic nucleus $$(z=50)$$ of radius $$9 \times 10^{-13} \mathrm{~cm}$$ is __________ $$\times 10^6 \mathrm{~V}$$.

JEE Main 2024 (Online) 27th January Evening Shift
19

A thin metallic wire having cross sectional area of $$10^{-4} \mathrm{~m}^2$$ is used to make a ring of radius $$30 \mathrm{~cm}$$. A positive charge of $$2 \pi \mathrm{~C}$$ is uniformly distributed over the ring, while another positive charge of 30 $$\mathrm{pC}$$ is kept at the centre of the ring. The tension in the ring is ______ $$\mathrm{N}$$; provided that the ring does not get deformed (neglect the influence of gravity). (given, $$\frac{1}{4 \pi \epsilon_0}=9 \times 10^9$$ SI units)

JEE Main 2024 (Online) 27th January Morning Shift
20

Three point charges $$\mathrm{q},-2 \mathrm{q}$$ and $$2 \mathrm{q}$$ are placed on $x$-axis at a distance $$x=0, x=\frac{3}{4} R$$ and $$x=R$$ respectively from origin as shown. If $$\mathrm{q}=2 \times 10^{-6} \mathrm{C}$$ and $$\mathrm{R}=2 \mathrm{~cm}$$, the magnitude of net force experienced by the charge $$-2 q$$ is ___________ N.

JEE Main 2023 (Online) 13th April Evening Shift Physics - Electrostatics Question 84 English

JEE Main 2023 (Online) 13th April Evening Shift
21

A thin infinite sheet charge and an infinite line charge of respective charge densities $$+\sigma$$ and $$+\lambda$$ are placed parallel at $$5 \mathrm{~m}$$ distance from each other. Points 'P' and 'Q' are at $$\frac{3}{\pi}$$ m and $$\frac{4}{\pi}$$ m perpendicular distances from line charge towards sheet charge, respectively. '$$\mathrm{E}_{\mathrm{P}}$$' and '$$\mathrm{E}_{\mathrm{Q}}$$' are the magnitudes of resultant electric field intensities at point 'P' and 'Q', respectively. If $$\frac{E_{p}}{E_{0}}=\frac{4}{a}$$ for $$2|\sigma|=|\lambda|$$, then the value of $$a$$ is ___________.

JEE Main 2023 (Online) 13th April Morning Shift
22

64 identical drops each charged upto potential of $$10 ~\mathrm{mV}$$ are combined to form a bigger drop. The potential of the bigger drop will be __________ $$\mathrm{mV}$$.

JEE Main 2023 (Online) 12th April Morning Shift
23

As shown in the figure, a configuration of two equal point charges $$\left(q_{0}=+2 \mu \mathrm{C}\right)$$ is placed on an inclined plane. Mass of each point charge is $$20 \mathrm{~g}$$. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height $$\mathrm{h}=x \times 10^{-3} \mathrm{~m}$$.

The value of $$x$$ is ____________.

(Take $$\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \mathrm{~N} \mathrm{~m}^{2} \mathrm{C}^{-2}, g=10 \mathrm{~m} \mathrm{~s}^{-2}$$ )

JEE Main 2023 (Online) 11th April Morning Shift Physics - Electrostatics Question 78 English

JEE Main 2023 (Online) 11th April Morning Shift
24

An electron revolves around an infinite cylindrical wire having uniform linear charge density $$2 \times 10^{-8} \mathrm{C} \mathrm{m}^{-1}$$ in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is ___________ $$\times 10^{6} \mathrm{~m} \mathrm{~s}^{-1}$$. Given mass of electron $$=9 \times 10^{-31} \mathrm{~kg}$$

JEE Main 2023 (Online) 10th April Evening Shift Physics - Electrostatics Question 76 English

JEE Main 2023 (Online) 10th April Evening Shift
25

Three concentric spherical metallic shells X, Y and Z of radius a, b and c respectively [a < b < c] have surface charge densities $$\sigma,-\sigma$$ and $$\sigma$$ respectively. The shells X and Z are at same potential. If the radii of X & Y are 2 cm and 3 cm, respectively. The radius of shell Z is _________ cm.

JEE Main 2023 (Online) 10th April Morning Shift
26

An electric dipole of dipole moment is $$6.0 \times 10^{-6} ~\mathrm{C m}$$ placed in a uniform electric field of $$1.5 \times 10^{3} ~\mathrm{NC}^{-1}$$ in such a way that dipole moment is along electric field. The work done in rotating dipole by $$180^{\circ}$$ in this field will be ___________ $$\mathrm{m J}$$.

JEE Main 2023 (Online) 8th April Morning Shift
27

A cubical volume is bounded by the surfaces $$\mathrm{x}=0, x=\mathrm{a}, y=0, y=\mathrm{a}, \mathrm{z}=0, z=\mathrm{a}$$. The electric field in the region is given by $$\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} x \hat{i}$$. Where $$\mathrm{E}_{0}=4 \times 10^{4} ~\mathrm{NC}^{-1} \mathrm{~m}^{-1}$$. If $$\mathrm{a}=2 \mathrm{~cm}$$, the charge contained in the cubical volume is $$\mathrm{Q} \times 10^{-14} \mathrm{C}$$. The value of $$\mathrm{Q}$$ is ________________.

(Take $$\epsilon_{0}=9 \times 10^{-12} ~\mathrm{C}^{2} / \mathrm{Nm}^{2}$$)

JEE Main 2023 (Online) 1st February Evening Shift
28

Two equal positive point charges are separated by a distance $$2 a$$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $$\mathrm{q}_{0}$$ becomes maximum is $$\frac{a}{\sqrt{x}}$$. The value of $$x$$ is __________.

JEE Main 2023 (Online) 1st February Morning Shift
29

Expression for an electric field is given by $$\overrightarrow{\mathrm{E}}=4000 x^{2} \hat{i} \frac{\mathrm{V}}{\mathrm{m}}$$. The electric flux through the cube of side $$20 \mathrm{~cm}$$ when placed in electric field (as shown in the figure) is __________ $$\mathrm{V} \mathrm{~cm}$$.

JEE Main 2023 (Online) 31st January Morning Shift Physics - Electrostatics Question 99 English

JEE Main 2023 (Online) 31st January Morning Shift
30
As shown in figure, a cuboid lies in a region with electric field $E=2 x^{2} \hat{i}-4 y \hat{j}+6 \hat{k} \mathrm{~N} / \mathrm{C}$. The magnitude of charge within the cuboid is $n \in_{0} C$.

The value of $n$ is _________ (if dimension of cuboid is $1 \times 2 \times 3 \mathrm{~m}^{3}$ )

JEE Main 2023 (Online) 30th January Evening Shift Physics - Electrostatics Question 97 English
JEE Main 2023 (Online) 30th January Evening Shift
31

For a charged spherical ball, electrostatic potential inside the ball varies with $$r$$ as $$\mathrm{V}=2ar^2+b$$.

Here, $$a$$ and $$b$$ are constant and r is the distance from the center. The volume charge density inside the ball is $$-\lambda a\varepsilon$$. The value of $$\lambda$$ is ____________.

$$\varepsilon$$ = permittivity of the medium

JEE Main 2023 (Online) 29th January Evening Shift
32

A point charge $$q_1=4q_0$$ is placed at origin. Another point charge $$q_2=-q_0$$ is placed at $$x=12$$ cm. Charge of proton is $$q_0$$. The proton is placed on $$x$$ axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is ___________ cm.

JEE Main 2023 (Online) 29th January Morning Shift
33

A uniform electric field of 10 N/C is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle ($$\theta$$) of deviation of the path of electron as it comes out of the field is ___________ (in degree).

JEE Main 2023 (Online) 25th January Morning Shift Physics - Electrostatics Question 89 English

JEE Main 2023 (Online) 25th January Morning Shift
34

A stream of a positively charged particles having $${q \over m} = 2 \times {10^{11}}{C \over {kg}}$$ and velocity $${\overrightarrow v _0} = 3 \times {10^7}\widehat i\,m/s$$ is deflected by an electric field $$1.8\widehat j$$ kV/m. The electric field exists in a region of 10 cm along $$x$$ direction. Due to the electric field, the deflection of the charge particles in the $$y$$ direction is _________ mm.

JEE Main 2023 (Online) 24th January Morning Shift
35

Two electric dipoles of dipole moments $$1.2 \times 10^{-30} \,\mathrm{Cm}$$ and $$2.4 \times 10^{-30} \,\mathrm{Cm}$$ are placed in two different uniform electric fields of strengths $$5 \times 10^{4} \,\mathrm{NC}^{-1}$$ and $$15 \times 10^{4} \,\mathrm{NC}^{-1}$$ respectively. The ratio of maximum torque experienced by the electric dipoles will be $$\frac{1}{x}$$. The value of $$x$$ is __________.

JEE Main 2022 (Online) 28th July Morning Shift
36

A long cylindrical volume contains a uniformly distributed charge of density $$\rho \,\mathrm{Cm}^{-3}$$. The electric field inside the cylindrical volume at a distance $$x=\frac{2 \varepsilon_{0}}{\rho} \mathrm{m}$$ from its axis is ________ $$\mathrm{Vm}^{-1}$$.

JEE Main 2022 (Online) 27th July Morning Shift Physics - Electrostatics Question 112 English

JEE Main 2022 (Online) 27th July Morning Shift
37

Three point charges of magnitude $$5 \mu \mathrm{C}, 0.16 \mu \mathrm{C}$$ and $$0.3 \mu \mathrm{C}$$ are located at the vertices $$A, B, C$$ of a right angled triangle whose sides are $$A B=3 \mathrm{~cm}, B C=3 \sqrt{2} \mathrm{~cm}$$ and $$C A=3 \mathrm{~cm}$$ and point $$A$$ is the right angle corner. Charge at point $$\mathrm{A}$$ experiences ____________ $$\mathrm{N}$$ of electrostatic force due to the other two charges.

JEE Main 2022 (Online) 26th July Evening Shift
38

The volume charge density of a sphere of radius $$6 \mathrm{~m}$$ is $$2 \,\mu \mathrm{C} \,\mathrm{cm}^{-3}$$. The number of lines of force per unit surface area coming out from the surface of the sphere is _______________ $$\times 10^{10} \,\mathrm{NC}^{-1}$$.

[Given : Permittivity of vacuum $$\epsilon_{0}=8.85 \times 10^{-12} \,\mathrm{C}^{2}\, \mathrm{~N}^{-1}-\mathrm{m}^{-2}$$ )

JEE Main 2022 (Online) 25th July Morning Shift
39

Eight similar drops of mercury are maintained at 12 V each. All these spherical drops combine into a single big drop. The potential energy of bigger drop will be ____________ E. Where E is the potential energy of a single smaller drop.

JEE Main 2022 (Online) 30th June Morning Shift
40

27 identical drops are charged at 22V each. They combine to form a bigger drop. The potential of the bigger drop will be _____________ V.

JEE Main 2022 (Online) 25th June Evening Shift
41
A particle of mass 1 mg and charge q is lying at the mid-point of two stationary particles kept at a distance '2 m' when each is carrying same charge 'q'. If the free charged particle is displaced from its equilibrium position through distance 'x' (x < < 1 m). The particle executes SHM. Its angular frequency of oscillation will be ____________ $$\times$$ 105 rad/s if q2 = 10 C2.
JEE Main 2021 (Online) 25th July Morning Shift
42
The total charge enclosed in an incremental volume of 2 $$\times$$ 10$$-$$9 m3 located at the origin is ___________ nC, if electric flux density of its field is found as

D = e$$-$$x sin y $$\widehat i$$ $$-$$ e$$-$$x cos y $$\widehat j$$ + 2z $$\widehat k$$ C/m2
JEE Main 2021 (Online) 22th July Evening Shift
43
A body having specific charge 8 $$\mu$$C/g is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V/m is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be _______________ s.

JEE Main 2021 (Online) 20th July Morning Shift Physics - Electrostatics Question 146 English
JEE Main 2021 (Online) 20th July Morning Shift
44
An infinite number of point charges, each carrying 1 $$\mu$$C charge, are placed along the y-axis at y = 1 m, 2 m, 4 m, 8 m ...............

The total force on a 1C point charge, placed at the origin, is x $$\times$$ 103 N.

The value of x, to the nearest integer, is __________. [Take $${1 \over {4\pi {\varepsilon _0}}} = 9 \times {10^9}$$ Nm2/C2]
JEE Main 2021 (Online) 18th March Evening Shift
45
The electric field in a region is given by $$\overrightarrow E = {2 \over 5}{E_0}\widehat i + {3 \over 5}{E_0}\widehat j$$ with $${E_0} = 4.0 \times {10^3}{N \over C}$$. The flux of this field through a rectangular surface area 0.4 m2 parallel to the Y-Z plane is __________ Nm2C$$-$$1.
JEE Main 2021 (Online) 17th March Evening Shift
46
27 similar drops of mercury are maintained at 10V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is __________ times that of a smaller drop.
JEE Main 2021 (Online) 26th February Evening Shift
47
Two identical conducting spheres with negligible volume have 2.1 nC and $$-$$0.1 nC charges, respectively. They are brought into contact and then separated by a distance of 0.5 m. The electrostatic force acting between the spheres is __________ $$\times$$ 10$$-$$9 N.

[Given : $$4\pi {\varepsilon _0} = {1 \over {9 \times {{10}^9}}}$$ SI unit]
JEE Main 2021 (Online) 25th February Evening Shift
48
Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.20 m. The charge on each of the sphere is $${a \over {21}} \times {10^{ - 8}}$$C. The value of 'a' will be ___________. [Given g = 10 ms$$-$$2]
JEE Main 2021 (Online) 25th February Evening Shift
49
The electric field in a region is given by $$\overrightarrow E = \left( {{3 \over 5}{E_0}\widehat i + {4 \over 5}{E_0}\widehat j} \right){N \over C}$$. The ratio of flux of reported field through the rectangular surface of area 0.2 m2 (parallel to y $$-$$ z plane) to that of the surface of area 0.3 m2 (parallel to x $$-$$ z plane) is a : b, where a = __________ [Here $${\widehat i}$$, $${\widehat j}$$ and $${\widehat k}$$ are unit vectors along x, y and z-axes respectively.]
JEE Main 2021 (Online) 25th February Morning Shift
50
512 identical drops of mercury are charged to a potential of 2V each. The drops are joined to form a single drop. The potential of this drop is ________ V.
JEE Main 2021 (Online) 25th February Morning Shift
51
A point charge of +12$$\mu$$C is at a distance 6 cm vertically above the centre of a square of side 12 cm as shown in figure. The magnitude of the electric flux through the square will be __________ $$\times$$ 103 Nm2/C.

JEE Main 2021 (Online) 24th February Evening Shift Physics - Electrostatics Question 160 English
JEE Main 2021 (Online) 24th February Evening Shift
52
An electric field $$\overrightarrow E = 4x\widehat i - \left( {{y^2} + 1} \right)\widehat j$$ N/C
passes through the box shown in figure. The
flux of the electric field through surfaces ABCD
and BCGF are marked as $${\phi _I}$$ and $${\phi _{II}}$$
respectively. The difference between $$\left( {{\phi _I} - {\phi _{II}}} \right)$$ is (in Nm2/C) _______. JEE Main 2020 (Online) 9th January Evening Slot Physics - Electrostatics Question 176 English
JEE Main 2020 (Online) 9th January Evening Slot

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