How many questions from Electric Field and Coulomb's Law appear in JEE?

Electric Field and Coulomb's Law has appeared in 133 of the last 186 JEE Main and JEE Advanced papers — about 72% of them — contributing 182 questions in total across those papers.

Is Electric Field and Coulomb's Law an important chapter for JEE?

Judged by how often it is actually tested, it appears in roughly 72% of papers. Chapters above about 50% are effectively guaranteed to show up every session, so they repay thorough preparation; lower-frequency chapters are better treated as targeted revision.

Where do these Electric Field and Coulomb's Law questions come from?

Every question is from an official JEE Main or JEE Advanced paper, transcribed from the original paper and tagged to this chapter. Answers follow the official answer key.

Electric Field and Coulomb's Law JEE Previous Year Questions with Answers

Q1·PhysicsMultiple correctJEE Advanced 2026

Consider an electric dipole comprising two charges

+q

and

-q

each with mass

m

, separated by a fixed distance

d

and initially at rest with its dipole moment pointing along

\hat{i}

. A uniform electric field

E\hat{j}

is turned on at time

t = 0

and it is turned off at

t = t_{f}

, when the dipole moment makes an angle

\theta_{f}

with

\hat{i}

. Neglecting any sources of energy loss, correct option(s) is/are:

(A)The center of mass of the dipole is deflected towards $\hat{j}$ in the presence of the field.
(B)If the magnitude of the final angular velocity $\omega_{f} = \sqrt{\frac{2qE}{md}}$ , then $\theta_{f} = \frac{\pi}{6}$ .
(C)If $\theta_{f} = \pi/3$ , then the change in kinetic energy of the dipole is given by $2\sqrt{3}\,qEd$ .
(D)For $\theta_{f} = \pi/4$ , the dipole rotates around its center of mass with a constant angular velocity after $t > t_{f}$ .

Q2·PhysicsSingle correctJEE Main 2026

Two point charges

q_1 = 3\,\mu C

and

q_2 = -4\,\mu C

are placed at points

(2\hat{i}+3\hat{j}+3\hat{k})

and

(\hat{i}+\hat{j}+\hat{k})

respectively. Force on charge

q_2

is ________ N.

\left(\text{Take } \dfrac{1}{4\pi\epsilon_0} = 9\times 10^{9}\text{ SI Units}\right)

(A) $(12\hat{i}+24\hat{j}+24\hat{k})\times 10^{-3}$
(B) $(4\hat{i}+8\hat{j}+8\hat{k})\times 10^{-3}$
(C) $(3\hat{i}+6\hat{j}+6\hat{k})\times 10^{-3}$
(D) $(-4\hat{i}-8\hat{j}-8\hat{k})\times 10^{-3}$

Q3·PhysicsSingle correctJEE Main 2026

A thin half ring of radius 35 cm is uniformly charged with a total charge of Q coulomb. If the magnitude of the electric field at centre of the half ring is 100 V/m, then the value of Q is ________ nC. (ε₀ = 8.85 × 10

^{-12}

C²/Nm² and π = 3.14)

(A)2.14
(B)2.44
(C)3.25
(D)0.7

Q4·PhysicsSingle correctJEE Main 2026

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field

\vec{E}_{1} = E_{0}\hat{x}

. If another electric field

\vec{E}_{2} = 2E_{0}(\hat{y} + \hat{z})

is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

(A)73%
(B)63%
(C)83%
(D)53%

Q5·PhysicsSingle correctJEE Main 2026

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: In electrostatics, a conductor does not store any net charge inside. Reason R: Inside the capacitor (with no dielectric medium), the free charge carriers, if placed between the plates of capacitor, experience force and drift. Choose the correct answer from the options given below

(A)Both A and R are true and R is the correct explanation of A
(B)Both A and R are true but R is NOT the correct explanation of A
(C)A is true but R is false
(D)A is false but R is true

Q6·PhysicsSingle correctJEE Main 2026

Two short electric dipoles

A

and

B

having dipole moment

p_{1}

and

p_{2}

respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point

x

is making an angle of 60° with the line joining points

O

and

x

. The ratio of the dipole moments

p_{2}/p_{1}

is ______.

(A) $\frac{\sqrt{3}}{2}$
(B) $2\sqrt{3}$
(C) $\frac{1}{\sqrt{3}}$
(D) $\sqrt{3}$

Q7·PhysicsSingle correctJEE Main 2026

Two point charges

8\,\mu C

and

-2\,\mu C

are located at

x = 2

cm and

x = 4

cm, respectively on the

x

-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is ________.

(A) $4 : 1$
(B) $3 : 4$
(C) $4 : 3$
(D) $4 : 5$

Q8·PhysicsSingle correctJEE Main 2026

Identify the correct statements : A. Electrostatic field lines form closed loops. B. The electric field lines point radially outward when charge is greater than zero. C. The Gauss-Law is valid only for inverse-square force. D. The workdone in moving a charged particle in a static electric field around a closed path is zero. E. The motion of a particle under Coulomb's force must take place in a plane. Choose the correct answer from the options given below :

(A)A, B, D, E Only
(B)A, B, C, D Only
(C)B, C, D, E Only
(D)A, C, E Only

Q9·PhysicsSingle correctJEE Main 2026

Three charges +2q. +3q and –4q are situated at (0,–3a), (2a, 0) and (–2a,0) respectively in the xy plane. The resultant dipole moment about origin is____

(A) $2qa\left(3\hat{j}-\hat{i}\right)$
(B) $2qa\left(3\hat{i}-7\hat{j}\right)$
(C) $2qa\left(7\hat{i}-3\hat{j}\right)$
(D) $2qa\left(3\hat{j}-7\hat{i}\right)$

Q10·PhysicsSingle correctJEE Main 2026

The electrostatic potential in a charged spherical region of radius r varies as

V = ar^{3} + b

, where a and b are constants. The total charge in the sphere of unit radius is

\alpha \times \pi a \in_{0}

. The value of

\alpha

is ______. (permittivity of vacuum is

\in_{0}

)

(A)–12
(B)–6
(C)–9
(D)–8

Q11·PhysicsNumericalJEE Main 2026

A point charge q = 1

\mu

C is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge

Q

= 24

\mu

C, distributed uniformly along its length, as shown in figure. Force between q and wire is ____ N. (Use

\frac{1}{4\pi\epsilon_0} = 9\times10^{9}\,\text{N.m}^{2}/\text{C}^{2}

)

Q12·PhysicsSingle correctJEE Main 2026

Two shorts dipoles

(A, B)

,

A

having charges ± 2μC and length 1 cm and

B

having charges ± 4μC and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point

P

, equi-distant from the centres of both dipoles is_____N/C.

(A) $\frac{9}{16}\sqrt{2}\times 10^{5}$
(B) $4.5\sqrt{2}\times 10^{4}$
(C) $9\sqrt{2}\times 10^{4}$
(D) $\frac{9}{16}\sqrt{2}\times 10^{4}$

Q13·PhysicsSingle correctJEE Main 2026

Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is :

(A) $\frac{3q}{\varepsilon_0}$
(B) $\frac{q}{\varepsilon_0}$
(C) $\frac{3q}{2\varepsilon_0}$
(D) $\frac{3q}{4\varepsilon_0}$

Q14·PhysicsSingle correctJEE Main 2026

A simple pendulum has a bob with mass

m

and charge q. The pendulum string has negligible mass. When a uniform and horizontal electric field

\vec{E}

is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is ______. (g : acceleration due to gravity)

(A) $mg - qE$
(B) $mg + qE$
(C) $\sqrt{m^2g^2 + q^2E^2}$
(D) $\sqrt{m^2g^2 - q^2E^2}$

Q15·PhysicsSingle correctJEE Main 2026

Six point charges are kept 60° apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the centre of the circle is _________. (

\in_{o}

is permittivity of free space)

(A) $-\frac{5Q}{8\pi \in_{o} R^{2}}(\hat{i}+\sqrt{3}\hat{j})$
(B) $-\frac{Q}{4\pi \in_{o} R^{2}}\left(\sqrt{3}\,\hat{i}-\hat{j}\right)$
(C) $-\left(\frac{5Q}{8\pi \in_{o} R^{2}}\right)\left(\hat{i}-3\hat{j}\right)$
(D) $\frac{Q}{4\pi \in_{o} R^{2}}\left(\sqrt{3}\,\hat{i}-\hat{j}\right)$

Q16·PhysicsSingle correctJEE Main 2026

Five positive charges each having charge

q

are placed at the vertices of a pentagon as shown in the figure. The electric potential

(V)

and the electric field

(\vec{E})

at the center O of the pentagon due to these five positive charges are :

(A) $V = \dfrac{5q}{4\pi\varepsilon_0 r}$ and $\vec{E} = 0$
(B) $V = \dfrac{5q}{4\pi\varepsilon_0 r}$ and $\vec{E} = \dfrac{5\sqrt{3}q}{8\pi\varepsilon_0 r^2}\,\hat{r}$
(C) $V = \dfrac{5q}{4\pi\varepsilon_0 r}$ and $\vec{E} = \dfrac{5q}{4\pi\varepsilon_0 r^2}\,\hat{r}$
(D) $V = 0$ and $\vec{E} = 0$

Q17·PhysicsSingle correctJEE Advanced 2025

Two co-axial conducting cylinders of same length

\ell

with radii

\sqrt{2}R

and 2R are kept, as shown in Fig. 1. The charge on the inner cylinder is Q and the outer cylinder is grounded. The annular region between the cylinders is filled with a material of dielectric constant κ =5. Consider an imaginary plane of the same length

\ell

at a distance R from the common axis of the cylinders. This plane is parallel to the axis of the cylinders. The cross-sectional view of this arrangement is shown in Fig. 2. Ignoring edge effects, the flux of the electric field through the plane is (

\varepsilon_0

is the permittivity of free space):

(A) $\frac{Q}{30\varepsilon_0}$
(B) $\frac{Q}{15\varepsilon_0}$
(C) $\frac{Q}{60\varepsilon_0}$
(D) $\frac{Q}{120\varepsilon_0}$

Q18·PhysicsMultiple correctJEE Advanced 2025

Six infinitely large and thin non-conducting sheets are fixed in configurations I and II. As shown in the figure, the sheets carry uniform surface charge densities which are indicated in terms of

\sigma_0

. The separation between any two consecutive sheets is 1 μm. The various regions between the sheets are denoted as 1, 2, 3, 4 and 5. If

\sigma_0 = 9

μC/m

^2

, then which of the following statements is/are correct: (Take permittivity of free space

\varepsilon_0 = 9\times 10^{-12}

F/m)

(A)In region 4 of the configuration I, the magnitude of the electric field is zero.
(B)In region 3 of the configuration II, the magnitude of the electric field is $\frac{\sigma_0}{\varepsilon_0}$ .
(C)Potential difference between the first and the last sheets of the configuration I is 5 V .
(D)Potential difference between the first and the last sheets of the configuration II is zero.

Q19·PhysicsSingle correctJEE Advanced 2025

List-I shows four configurations, each consisting of a pair of ideal electric dipoles. Each dipole has a dipole moment of magnitude p, oriented as marked by arrows in the figures. In all the configurations the dipoles are fixed such that they are at a distance 2r apart along the x direction. The midpoint of the line joining the two dipoles is X. The possible resultant electric fields

\vec{E}

at X are given in List-II. Choose the option that describes the correct match between the entries in List-I to those in List-II.

List-I	List-II
P.see figure	1. $\vec{E} = 0$
Q.see figure	2. $\vec{E} = -\frac{p}{2\pi\varepsilon_{0}r^{3}}\hat{j}$
R.see figure	3. $\vec{E} = -\frac{p}{4\pi\varepsilon_{0}r^{3}}(\hat{i} - \hat{j})$
S.see figure	4. $\vec{E} = \frac{p}{4\pi\varepsilon_{0}r^{3}}(2\hat{i} - \hat{j})$
	5. $\vec{E} = \frac{p}{\pi\varepsilon_{0}r^{3}}\hat{i}$

(A)(P) → (3), (Q) → (1), (R) → (2), (S) → (4)
(B)(P) → (4), (Q) → (5), (R) → (3), (S) → (1)
(C)(P) → (2), (Q) → (1), (R) → (4), (S) → (5)
(D)(P) → (2), (Q) → (1), (R) → (3), (S) → (5)

Q20·PhysicsSingle correctJEE Main 2025

Electric charge is transferred to an irregular metallic disk as shown in 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: (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

(A)A, B and C Only
(B)A and C Only
(C)D and E Only
(D)B and C Only

Q21·PhysicsSingle correctJEE Main 2025

An infinitely long wire has uniform linear charge density

\lambda=2\ nC/m

. The net flux through a Gaussian cube of side length

\sqrt3

cm, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be

x\ Nm^2C^{-1}

, where

x

is: [Neglect any edge effects and use

\dfrac{1}{4\pi\varepsilon_0}=9\times10^9

SI units]

(A) $0.72\pi$
(B) $1.44\pi$
(C) $6.48\pi$
(D) $2.16\pi$

Q22·PhysicsSingle correctJEE Main 2025

Two metal spheres of radius

R

and

3R

have same surface charge density

\sigma

. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes

\sigma_1

and

\sigma_2

, respectively. The ratio

\dfrac{\sigma_1}{\sigma_2}

is:

(A) $\dfrac{1}{9}$
(B) $9$
(C) $\dfrac{1}{3}$
(D) $3$

Q23·PhysicsIntegerJEE Main 2025

The electric field in a region is given by

\vec{E}=\left(2\hat{i}+4\hat{j}+6\hat{k}\right)\times10^{3}

N/C. The flux of the field through a rectangular surface parallel to the x-z plane is

6.0

Nm

^2

C

^{-1}

. The area of the surface is __________ cm

^2

.

Q24·PhysicsSingle correctJEE Main 2025

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:

(A)Both (A) and (R) are correct and (R) is the correct explanation of (A)
(B)(A) is correct but (R) is not correct
(C)Both (A) and (R) are correct but (R) is not correct explanation of (A)
(D)(A) is not correct but (R) is correct

Q25·PhysicsSingle correctJEE Main 2025

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 with a potential difference of 5 V applied. Separation between the plates is 0.5 mm. If the dipole is rotated by

30^\circ

from the axis, it tends to realign in the direction due to a torque. The value of torque is:

(A) $5\times10^{-9}$ Nm
(B) $5\times10^{-3}$ Nm
(C) $2.5\times10^{-12}$ Nm
(D) $2.5\times10^{-9}$ Nm

Q26·PhysicsSingle correctJEE Main 2025

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 A, B, C and D points is:

(A) $\vec{E}_A=\vec{E}_B$ ; $\vec{E}_C=\vec{E}_D$
(B) $\vec{E}_A>\vec{E}_B$ ; $\vec{E}_C=\vec{E}_D$
(C) $\vec{E}_C\ne\vec{E}_D$ ; $\vec{E}_A>\vec{E}_B$
(D) $|\vec{E}_A|=|\vec{E}_B|$ ; $\vec{E}_C>\vec{E}_D$

Q27·PhysicsSingle correctJEE Main 2025

Two small spherical balls of mass 10 g each with charges

-2\,\mu C

and

2\,\mu C

, are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite non-conducting charge sheet with uniform charge density of

100\,\mu C/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_0:8.85\times10^{-12}

C

^2

/Nm

^2

)

(A)112 Nm
(B)1.12 Nm
(C)2.24 Nm
(D)11.2 Nm

Q28·PhysicsSingle correctJEE Main 2025

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

(A) $2E$
(B) $\sqrt2\,E$
(C) $\dfrac{E}{2}$
(D)Zero

Q29·PhysicsSingle correctJEE Main 2025

Consider a circular loop that is uniformly charged and has a radius

a\sqrt2

. Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum, if the ring is assumed to be placed in the xy-plane at the origin:

(A) $\dfrac{a}{\sqrt2}$
(B) $\dfrac{a}{2}$
(C) $a$
(D) $0$

Q30·PhysicsSingle correctJEE Main 2025

A small bob of mass 100 mg and charge

+10\ \mu 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 the string subtends an angle of

45^\circ

with the sheet at equilibrium, the charge density of the sheet will be: (Given

\varepsilon_0=8.85\times10^{-12}

F/m and acceleration due to gravity

g=10

m/s

^2

)

(A)0.885 nC/m $^2$
(B)17.7 nC/m $^2$
(C)885 nC/m $^2$
(D)1.77 nC/m $^2$

Q31·PhysicsSingle correctJEE Main 2025

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:

(A) $\dfrac{\sigma q}{4\varepsilon_0}$
(B) $\dfrac{3\sigma q}{2\varepsilon_0}$
(C) $\dfrac{3\sigma q}{4\varepsilon_0}$
(D) $\dfrac{\sigma q}{2\varepsilon_0}$

Q32·PhysicsSingle correctJEE Main 2025

A point charge

+q

is placed at the origin. A second point charge

+9q

is placed at

(d,0,0)

in Cartesian coordinate system. The point in between them where the electric field vanishes is:

(A) $\left(\dfrac{4d}{3},0,0\right)$
(B) $\left(\dfrac{d}{4},0,0\right)$
(C) $\left(\dfrac{3d}{4},0,0\right)$
(D) $\left(\dfrac{d}{3},0,0\right)$

Q33·PhysicsSingle correctJEE Main 2025

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:

(A)(A) is correct but (R) is not correct
(B)Both (A) and (R) are correct but (R) is not the correct explanation of (A)
(C)Both (A) and (R) are correct and (R) is the correct explanation of (A)
(D)(A) is not correct but (R) is correct

Q34·PhysicsSingle correctJEE Main 2025

A point charge causes an electric flux of

-2\times 10^4

Nm²C⁻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

\varepsilon_0=8.85\times 10^{-12}

C²N⁻¹m⁻²)

(A) $-17.7\times 10^{-8}$ C
(B) $-15.7\times 10^{-8}$ C
(C) $17.7\times 10^{-8}$ C
(D) $15.7\times 10^{-8}$ C

Q35·PhysicsSingle correctJEE Main 2025

An electric dipole of mass m, charge q, and length

l

is placed in a uniform electric field

\vec{E}=E_0\hat{i}

. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:

(A) $\dfrac{1}{2\pi}\sqrt{\dfrac{2ml}{qE_0}}$
(B) $2\pi\sqrt{\dfrac{ml}{qE_0}}$
(C) $\dfrac{1}{2\pi}\sqrt{\dfrac{ml}{2qE_0}}$
(D) $2\pi\sqrt{\dfrac{ml}{2qE_0}}$

Q36·PhysicsSingle correctJEE Main 2025

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density

\sigma_0

(orientation as shown in the figure). Choose the correct option from the following.

(A)Torque on dipole is zero and net force is directed away from the sheet.
(B)Torque on dipole is zero and net force acts towards the sheet.
(C)Potential energy of dipole is minimum and torque is zero.
(D)Potential energy and torque both are maximum.

Q37·PhysicsSingle correctJEE Main 2025

Match List-I with List-II. Choose the correct answer from the options given below:

List-I	List-II
A.Electric field inside (distance r > 0 from center) of a uniformly charged spherical shell with surface charge density σ, radius R	I. $\dfrac{\sigma}{\varepsilon_0}$
B.Electric field at distance r > 0 from a uniformly charged infinite plane sheet with surface charge density σ	II. $\dfrac{\sigma}{2\varepsilon_0}$
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. $\dfrac{\sigma R^2}{\varepsilon_0 r^2}$

(A)(A)-(IV), (B)-(II), (C)-(III), (D)-(II)
(B)(A)-(IV), (B)-(II), (C)-(III), (D)-(I)
(C)(A)-(III), (B)-(II), (C)-(IV), (D)-(I)
(D)(A)-(III), (B)-(II), (C)-(IV), (D)-(II)

Q38·PhysicsIntegerJEE Main 2025

An electric dipole of dipole moment

6\times10^{-6}

Cm is placed in uniform electric field of magnitude

10^6

V/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.

Q39·PhysicsSingle correctJEE Main 2025

A particle of mass "m" and charge "q" is fastened to one end "A" of a massless string having equilibrium length

\ell

, 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

(A) $\sqrt{\frac{2qE\ell}{m}}$
(B) $\sqrt{\frac{qE\ell}{4m}}$
(C) $\sqrt{\frac{qE\ell}{m}}$
(D) $\sqrt{\frac{qE\ell}{2m}}$

Q40·PhysicsSingle correctJEE Main 2025

A small uncharged conducting sphere is placed in contact with an identical sphere but having

4\times10^{-8}

C charge and then removed to a distance such that the force of repulsion between them is

9\times10^{-3}

N. The distance between them is (Take

\dfrac{1}{4\pi\varepsilon_0}

as

9\times10^9

in SI units):

(A)2 cm
(B)3 cm
(C)4 cm
(D)1 cm

Q41·PhysicsIntegerJEE Main 2025

A square loop of sides a = 1 m is held normally in front of a point charge q = 1C. The flux of the electric field through the shaded region is

\dfrac{5}{p}\times\dfrac{1}{\varepsilon_0}

Nm

^2

/C, where the value of p is _______.

Q42·PhysicsSingle correctJEE Main 2025

Two point charges

-4\,\mu c

and

4\,\mu c

, constituting an electric dipole, are placed at

(-9, 0, 0)

cm and

(9, 0, 0)

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 :

(A) $14.4$ mJ
(B) $18.4$ mJ
(C) $12.4$ mJ
(D) $16.4$ mJ

Q43·PhysicsSingle correctJEE Main 2025

The electric flux is

\phi=\alpha\sigma+\beta\lambda

where

\lambda

and

\sigma

are linear and surface charge density, respectively.

\left(\dfrac{\alpha}{\beta}\right)

represents

(A)charge
(B)electric field
(C)displacement
(D)area

Q44·PhysicsSingle correctJEE Main 2025

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 charges q separated by a distance 2a. For the charge particle at P not to experience any net force, which of the following correctly describes the situation?

(A) $\dfrac{a}{r}\sim 20$
(B) $\dfrac{a}{r}\sim 10$
(C) $\dfrac{a}{r}\sim 0.5$
(D) $\dfrac{a}{r}\sim 3$

Q45·PhysicsSingle correctJEE Main 2025

A line charge of length a/2 is kept at the centre of an edge BC of a cube ABCDEFGH having edge length a (see figure). If the linear charge density of the line is λ C per unit length, then the total electric flux through all the faces of the cube is: (take ε₀ = free-space permittivity)

(A)λa/8ε₀
(B)λa/16ε₀
(C)λa/2ε₀
(D)λa/4ε₀

Q46·PhysicsSingle correctJEE Main 2025

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

(A) $\frac{V_0}{2}$ and $\frac{E_0}{16}$
(B)zero and $\frac{E_0}{8}$
(C)zero and $\frac{E_0}{16}$
(D) $V_0$ and $\frac{E_0}{4}$

Q47·PhysicsNumericalJEE Advanced 2024

A charge is kept at the central point P of a cylindrical region. The two edges subtend a half-angle θ at P, as shown in the figure. When θ = 30°, then the electric flux through the curved surface of the cylinder is Φ. If θ = 60°, then the electric flux through the curved surface becomes

\frac{\phi}{\sqrt{n}}

, where the value of n is ______

Q48·PhysicsMultiple correctJEE Advanced 2024

A small electric dipole

\vec{p}_0

, having a moment of inertia I about its center, is kept at a distance r from the center of a spherical shell of radius R . The surface charge density σ is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle θ as shown in the figure. While staying at a distance r , the dipole is free to rotate about its center. If released from rest, then which of the following statement(s) is(are) correct? [ε₀ is the permittivity of free space.]

(A)The dipole will undergo small oscillations at any finite value of r .
(B)The dipole will undergo small oscillations at any finite value of r > R .
(C)The dipole will undergo small oscillations with an angular frequency of $\sqrt{\frac{2\sigma p_0}{\varepsilon_0 I}}$ at r = 2R .
(D)The dipole will undergo small oscillations with an angular frequency $\sqrt{\frac{\sigma p_0}{100\varepsilon_0 I}}$ at r = 10R .

Q49·PhysicsSingle correctJEE Main 2024

Five charges

+q

,

+5q

,

-2q

,

+3q

and

-4q

are situated as shown in the figure. The electric flux due to this configuration through the surface S is:

(A) $\dfrac{5q}{\varepsilon_{0}}$
(B) $\dfrac{4q}{\varepsilon_{0}}$
(C) $\dfrac{3q}{\varepsilon_{0}}$
(D) $\dfrac{q}{\varepsilon_{0}}$

Q50·PhysicsNumericalJEE Main 2024

At the centre of a half ring of radius

R=10

cm and linear charge density

4n\ \mathrm{C\ m^{-1}}

, the potential is

x\,\pi\ \mathrm{V}

. The value of

x

is ______.

Q51·PhysicsNumericalJEE Main 2024

An electric field

\vec{E}=(2x\hat{i})

N/C exists in space. A cube of side 2 m is placed in the space with its edges parallel to the coordinate axes and one corner at the origin. The electric flux through the cube is _______ N m

^{2}

/C.

Q52·PhysicsNumericalJEE Main 2024

An electric field,

\vec E=\dfrac{2\hat i+6\hat j+8\hat k}{\sqrt6}

passes through the surface of

4\,m^2

area having unit vector

\hat n=\left(\dfrac{2\hat i+\hat j+\hat k}{\sqrt6}\right)

. The electric flux for that surface is ___ V m.

Q53·PhysicsNumericalJEE Main 2024

If the net electric field at point P along the Y axis is zero, then the ratio of

\dfrac{q_2}{q_3}

is

\dfrac{8}{5x}

, where x = ________ .

Q54·PhysicsNumericalJEE Main 2024

Three infinitely long charged thin sheets are placed as shown in the figure. The magnitude of the electric field at the point

P

is

\tfrac{x\sigma}{\varepsilon_{0}}

. The value of

x

is _______. (all quantities are measured in SI units)

Q55·PhysicsSingle correctJEE Main 2024

\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:

(A) $\tfrac{\sigma}{\varepsilon_{0}}R$
(B) $\tfrac{\sigma}{2\varepsilon_{0}}$
(C) $\tfrac{\sigma}{\varepsilon_{0}}$
(D) $\tfrac{\sigma}{4\varepsilon_{0}}$

Q56·PhysicsSingle correctJEE Main 2024

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

(A)4 N
(B)6 N
(C)1 N
(D)12 N

Q57·PhysicsNumericalJEE Main 2024

The electric field at a point P, at a distance

r

on the axial line of a short electric dipole, is E. The electric field at a point R, at a distance

2r

on the equatorial line of the same dipole, will be

\dfrac{E}{x}

. The value of

x

is __________.

Q58·PhysicsSingle correctJEE Main 2024

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

(A)To conduct excess charge due to air friction to the ground and prevent sparking.
(B)To alert other vehicles.
(C)To protect tyres from catching dirt from the ground.
(D)It is a custom.

Q59·PhysicsNumericalJEE Main 2024

An infinite plane sheet of charge having uniform surface charge density

+\sigma_s\,C/m^2

is placed on x-y plane. Another infinitely long line charge having uniform linear charge density

+\lambda_s\,C/m

is placed at

z=4\,m

plane and parallel to y-axis. If the magnitude when

|\sigma_s|=2|\lambda_s|

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 ___

Q60·PhysicsSingle correctJEE Main 2024

An infinitely long positively charged straight thread has a linear charge density

\lambda\,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:

(A)(1)
(B)(2)
(C)(3)
(D)(4)

Q61·PhysicsSingle correctJEE Main 2024

A charge

q

is placed at the center of one of the surface of a cube. The flux linked with the cube is

(A) $\tfrac{q}{4\varepsilon_0}$
(B) $\tfrac{q}{2\varepsilon_0}$
(C) $\tfrac{q}{8\varepsilon_0}$
(D)Zero

Q62·PhysicsSingle correctJEE Main 2024

C_1

and

C_2

are two hollow concentric cubes enclosing charges

2Q

and

3Q

respectively as shown in figure. The ratio of electric flux passing through

C_1

and

C_2

is:

(A)2:5
(B)5:2
(C)2:3
(D)3:2

Q63·PhysicsNumericalJEE Main 2024

Suppose a uniformly charged wall provides a uniform electric field of

2\times 10^4

N/C normally. A charged particle of mass 2 g being suspended through a silk thread of length 20 cm and remain stayed at a distance of 10 cm from the wall. Then the charge on the particle will be

\dfrac{1}{\sqrt x}\,\mu

C where

x=

__________. [use

g=10

m/s

^2

]

Q64·PhysicsSingle correctJEE Main 2024

Two charges q and 3q 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 :

(A) $\dfrac{(1+\sqrt{3})}{r}$
(B) $\dfrac{r}{3(1+\sqrt{3})}$
(C) $\dfrac{r}{(1+\sqrt{3})}$
(D) $r(1+\sqrt{3})$

Q65·PhysicsSingle correctJEE Main 2024

A particle of charge

-q

and mass

m

moves in a circle of radius

r

around an infinitely long line charge of linear density

+\lambda

. Then time period will be given as: (Consider

k

as Coulomb's constant)

(A) $T^2=\dfrac{4\pi^2 m}{2k\lambda q}r^3$
(B) $T=2\pi r\sqrt{\dfrac{m}{2k\lambda q}}$
(C) $T=\dfrac{1}{2\pi r}\sqrt{\dfrac{m}{2k\lambda q}}$
(D) $T=\dfrac{1}{2\pi}\sqrt{\dfrac{2k\lambda q}{m}}$

Q66·PhysicsSingle correctJEE Main 2024

Two charges of

5Q

and

-2Q

are situated at the points

(3a,0)

and

(-5a,0)

respectively. The electric flux through a sphere of radius

4a

having center at origin is :

(A) $\dfrac{2Q}{\epsilon_0}$
(B) $\dfrac{5Q}{\epsilon_0}$
(C) $\dfrac{7Q}{\epsilon_0}$
(D) $\dfrac{3Q}{\epsilon_0}$

Q67·PhysicsNumericalJEE Main 2024

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density

+\sigma

. The electron at

t=0

is at a distance of 1 m from S and has a speed of 1 m/s. The maximum value of

\sigma

if the electron strikes S at

t=1

s is

\alpha\left[\dfrac{m\epsilon_0}{e}\right]\dfrac{C}{m^2}

the value of

\alpha

is ______ .

Q68·PhysicsSingle correctJEE Main 2024

An electric field is given by

(6\hat{i}+5\hat{j}+3\hat{k})

N/C. The electric flux through a surface area

30\hat{i}

m

^{2}

lying in YZ-plane (in SI unit) is:

(A)90
(B)150
(C)180
(D)60

Q69·PhysicsNumericalJEE Main 2024

Two charges of

-4\,\mu

C and

+4\,\mu

C are placed at the points A(1,0,4) m and B(2,-1,5) m located in an electric field

\vec E=0.20\,\hat i

V/cm. The magnitude of the torque acting on the dipole is

8\sqrt\alpha\times10^{-5}

Nm. Where

\alpha

is ________.

Q70·PhysicsNumericalJEE Main 2024

A thin metallic wire having cross sectional area of

10^{-4}

m

^2

is used to make a ring of radius 30 cm. A positive charge of

2\pi

C is uniformly distributed over the ring, while another positive charge of 30 pC is kept at the centre of the ring. The tension in the ring is __________ N; provided that the ring does not get deformed (neglect the influence of gravity). (given,

\dfrac{1}{4\pi\epsilon_0}=9\times 10^9

SI units).

Q71·PhysicsSingle correctJEE Main 2023

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 :

(A) $r$
(B) $\frac{1}{r}$
(C) $\frac{1}{r^{3}}$
(D) $\frac{1}{r^{2}}$

Q72·PhysicsSingle correctJEE Main 2023

A 10

\mu

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

(A)9 $\mu$ C, 1 $\mu$ C
(B)5 $\mu$ C, 5 $\mu$ C
(C)7 $\mu$ C, 3 $\mu$ C
(D)8 $\mu$ C, 2 $\mu$ C

Q73·PhysicsNumericalJEE Main 2023

A thin infinite sheet charge and an infinite line charge of respective charge densities

+\sigma

and

+\lambda

are placed parallel at

5\,m

distance from each other. Points 'P' and 'Q' are at

\dfrac{3}{\pi}\,m

and

\dfrac{4}{\pi}\,m

perpendicular distance from line charge towards sheet charge, respectively.

'E_{P}'

and

'E_{Q}'

are the magnitudes of resultant electric field intensities at point 'P' and 'Q', respectively. If

\dfrac{E_{P}}{E_{Q}}=\dfrac{4}{a}

for

2|\sigma|=|\lambda|

. Then the value of

a

is _____.

Q74·PhysicsNumericalJEE Main 2023

Three point charges

q

,

-2q

and

2q

are placed on x-axis at a distance

x = 0

,

x = \dfrac{3}{4}R

and

x = R

respectively from origin as shown. If

q = 2 \times 10^{-6}

C and R = 2 cm, the magnitude of net force experienced by the charge

-2q

is ____ N.

Q75·PhysicsSingle correctJEE Main 2023

Two charges each of magnitude

0.01\,C

and separated by a distance of

0.4\,m

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 the dipole is:

(A) $4.0\times10^{-5}\,Nm$
(B) $2.0\times10^{-5}\,Nm$
(C) $4.0\times10^{-8}\,Nm$
(D) $1.5\times10^{-5}\,Nm$

Q76·PhysicsNumericalJEE Main 2023

As shown in the figure. a configuration of two equal point charges (

q_0 = +2\mu

C) is placed on an inclined plane. Mass of each point charge is 20 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

h = x \times 10^{-3}

m The value of x is ____. (Take

\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9 \text{ N m}^2\text{C}^{-2}, g = 10 \text{ ms}^{-1}

)

Q77·PhysicsNumericalJEE Main 2023

An electron revolves around an infinite cylindrical wire having uniform linear charge density

2\times10^{-8}

Cm

^{-1}

in a circular path under the influence of the attractive electrostatic field as shown in the figure. The velocity with which it is revolving is

9\times10^{x}

m/s. (Given mass of electron

=9\times10^{-31}

kg). The value of x is _______ .

Q78·PhysicsNumericalJEE Main 2023

An electric dipole of dipole moment is

6.0\times10^{-6}\,\text{Cm}

placed in a uniform electric field of

1.5\times10^{3}\,\text{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 ______

\text{mJ}

Q79·PhysicsSingle correctJEE Main 2023

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

(A)(1)
(B)(2)
(C)(3)
(D)(4)

Q80·PhysicsSingle correctJEE Main 2023

A dipole comprises of two charged particles of identical magnitude

q

and opposite in nature. The mass '

m

' of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance '

l

'. If the dipole is placed in a uniform electric field '

\vec{E}

' in such a way that dipole axis makes a very small angle with the electric field '

\vec{E}

'. The angular frequency of the oscillations of the dipole when released is given by:

(A) $\sqrt{\dfrac{8qE}{3ml}}$
(B) $\sqrt{\dfrac{4qE}{ml}}$
(C) $\sqrt{\dfrac{4qE}{3ml}}$
(D) $\sqrt{\dfrac{8qE}{ml}}$

Q81·PhysicsNumericalJEE Main 2023

A cubical volume is bounded by the surfaces

x=0,\ x=a,\ y=0,\ y=a,\ z=0,\ z=a

. The electric field in the region is given by

\vec E=E_0 x\hat i

, where

E_0=4\times10^4\,NC^{-1}m^{-1}

. If

a=2

cm, the charge contained in the cubical volume is

Q\times10^{-14}

C. The value of Q is _________. (Take

\varepsilon_0=9\times10^{-12}\,C^2/Nm^2

)

Q82·PhysicsNumericalJEE Main 2023

Two equal positive point charges are separated by a distance

2a

. 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

q_0

becomes maximum is

\tfrac{a}{\sqrt{x}}

. The value of

x

is _______ .

Q83·PhysicsSingle correctJEE Main 2023

Let

\sigma

be the uniform surface charge density of two infinite thin plane sheets shown in the figure. Then the electric fields in three different regions

E_I

,

E_{II}

and

E_{III}

are:

(A) $\vec{E}_I=\tfrac{2\sigma}{\varepsilon_0}\hat{n},\ \vec{E}_{II}=0,\ \vec{E}_{III}=\tfrac{2\sigma}{\varepsilon_0}\hat{n}$
(B) $\vec{E}_I=\tfrac{\sigma}{2\varepsilon_0}\hat{n},\ \vec{E}_{II}=0,\ \vec{E}_{III}=\tfrac{\sigma}{2\varepsilon_0}\hat{n}$
(C) $\vec{E}_I=-\tfrac{\sigma}{\varepsilon_0}\hat{n},\ \vec{E}_{II}=0,\ \vec{E}_{III}=\tfrac{\sigma}{\varepsilon_0}\hat{n}$
(D) $\vec{E}_I=0,\ \vec{E}_{II}=\tfrac{\sigma}{\varepsilon_0}\hat{n},\ \vec{E}_{III}=0$

Q84·PhysicsSingle correctJEE Main 2023

Considering a group of positive charges, which of the following statements is correct?

(A)both the net potential and the net electric field cannot be zero at a point.
(B)net potential of the system at a point can be zero but net electric field can't be zero at that point.
(C)net potential of the system cannot be zero at a point but net electric field can be zero at that point.
(D)Both the net potential and the net field can be zero at a point.

Q85·PhysicsNumericalJEE Main 2023

Expression for an electric field is given by

\vec{E} = 4000\,x^2\,\hat{i}\,\frac{\text{V}}{\text{m}}

. The electric flux through the cube of side

20

cm when placed in electric field (as shown in the figure) is __________ V cm.

Q86·PhysicsSingle correctJEE Main 2023

Electric field in a certain region is given by

\vec E=\left(\dfrac{A}{x^2}\hat i+\dfrac{B}{y^3}\hat j\right)

. The SI unit of A and B are:

(A) $Nm^3C^{-1};\ Nm^2C^{-1}$
(B) $Nm^2C^{-1};\ Nm^3C^{-1}$
(C) $Nm^3C;\ Nm^2C$
(D) $Nm^2C;\ Nm^3C$

Q87·PhysicsSingle correctJEE Main 2023

A point charge

Q

is placed at the centre of a conducting spherical shell of inner radius

a

and outer radius

b

. The electric field due to charge

Q

in the three regions I (

r<a

), II (

a<r<b

) and III (

r>b

) is given by:

(A) $E_I=0,\ E_{II}=0,\ E_{III}=0$
(B) $E_I=0,\ E_{II}=0,\ E_{III}\neq0$
(C) $E_I\neq0,\ E_{II}=0,\ E_{III}\neq0$
(D) $E_I\neq0,\ E_{II}=0,\ E_{III}=0$

Q88·PhysicsNumericalJEE Main 2023

A cuboid with one corner at the origin and edges of length 1 m, 2 m and 3 m along the x, y and z axes respectively lies in a region with electric field

\vec{E}=2x^{2}\hat{i}-4y\hat{j}+6\hat{k}

N/C. The magnitude of charge within the cuboid is

n\varepsilon_0

C. The value of

n

is _______.

Q89·PhysicsNumericalJEE Main 2023

A point charge

q_1 = 4q_0

is placed at the origin. Another point charge

q_2 = -q_0

is placed at

x = 12

cm. The charge of a proton is

q_0

. The proton is placed on the 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.

Q90·PhysicsSingle correctJEE Main 2023

In a cuboid of dimension

2L \times 2L \times L

, a charge

q

is placed at the center of the surface '

S

' having area

4L^2

. The flux through the opposite surface to '

S

' is given by:

(A) $\dfrac{q}{12\varepsilon_0}$
(B) $\dfrac{q}{6\varepsilon_0}$
(C) $\dfrac{q}{3\varepsilon_0}$
(D) $\dfrac{q}{2\varepsilon_0}$

Q91·PhysicsNumericalJEE Main 2023

For a charged spherical ball, electrostatic potential inside the ball varies with

r

as

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

Q92·PhysicsNumericalJEE Main 2023

A uniform electric field of 10 N/C is created between two parallel charged plates. 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 the electron as it comes out of the field is _______ (in degree).

Q93·PhysicsSingle correctJEE Main 2023

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?

(A) $x = -4$ cm
(B) $x = 6$ cm
(C) $x = 4$ cm
(D) $x = 8$ cm

Q94·PhysicsSingle correctJEE Main 2023

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?

(A) $2d\sqrt{K}$
(B) $1.5\,d\sqrt{K}$
(C) $d\sqrt{K}$
(D) $K\sqrt{d}$

Q95·PhysicsNumericalJEE Main 2023

A stream of positively charged particles having

\tfrac{q}{m}=2\times10^{11}\,\tfrac{\text{C}}{\text{kg}}

and velocity

\vec{v}_0=3\times10^7\,\hat{i}

m/s is deflected by an electric field

1.8\,\hat{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.

Q96·PhysicsMultiple correctJEE Advanced 2022

Six charges are placed around a regular hexagon of side length a as shown in the figure. Five of them have charge q , and the remaining one has charge x . The perpendicular from each charge to the nearest hexagon side passes through the center O of the hexagon and is bisected by the side. Which of the following statement(s) is(are) correct in SI units?

(A)When x = q , the magnitude of the electric field at O is zero.
(B)When x = $-$ q , the magnitude of the electric field at O is $\frac{q}{6\pi \epsilon_0 a^2}$
(C)When x = 2q, the potential at O is $\frac{7q}{4\sqrt{3}\pi \epsilon_0 a}$ .
(D)When x = $-$ 3q , the potential at O is $-\frac{3q}{4\sqrt{3}\pi \epsilon_0 a}$

Q97·PhysicsIntegerJEE Advanced 2022

A charge q is surrounded by a closed surface consisting of an inverted cone of height h and base radius R , and a hemisphere of radius R as shown in the figure. The electric flux through the conical surface is

\frac{nq}{6\epsilon_0}

(in SI units). The value of n is_________

Q98·PhysicsMultiple correctJEE Advanced 2022

In the figure, the inner (shaded) region

A

represents a sphere of radius

r_A = 1

, within which the electrostatic charge density varies with the radial distance

r

from the center as

\rho_A = kr

, where

k

is positive. In the spherical shell

B

of outer radius

r_B

, the electrostatic charge density varies as

\rho_B = \frac{2k}{r}

. Assume that dimensions are taken care of. All physical quantities are in their SI units. Which of the following statement(s) is(are) correct?

(A)If $r_B = \sqrt{\frac{3}{2}}$ , then the electric field is zero everywhere outside $B$ .
(B)If $r_B = \frac{3}{2}$ , then the electric potential just outside $B$ is $\frac{k}{\epsilon_0}$ .
(C)If $r_B = 2$ , then the total charge of the configuration is $15\pi k$ .
(D)If $r_B = \frac{5}{2}$ , then the magnitude of the electric field just outside $B$ is $\frac{13\pi k}{\epsilon_0}$ .

Q99·PhysicsSingle correctJEE Main 2022

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 :

(A) $\frac{\rho_{0}r}{4\varepsilon_{0}}\left(\frac{3}{4} - \frac{r}{R}\right)$
(B) $\frac{\rho_{0}r}{3\varepsilon_{0}}\left(\frac{3}{4} - \frac{r}{R}\right)$
(C) $\frac{\rho_{0}r}{4\varepsilon_{0}}\left(1 - \frac{r}{R}\right)$
(D) $\frac{\rho_{0}r}{5\varepsilon_{0}}\left(1 - \frac{r}{R}\right)$

Q100·PhysicsSingle correctJEE Main 2022

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

(A)3F/2
(B)3F/4
(C)F
(D)2F

Q101·PhysicsNumericalJEE Main 2022

Two electric dipoles of dipole moments 1.2 × 10

^{-30}

cm and 2.4 × 10

^{-30}

cm are placed in two difference uniform electric fields of strengths 5 × 10

^{4}

NC

^{-1}

and 15 × 10

^{4}

NC

^{-1}

respectively. The ratio of maximum torque experienced by the electric dipoles will be

\frac{1}{x}

. The value of x is ________.

Q102·PhysicsSingle correctJEE Main 2022

A uniform electric field E = (8m/e) V/m is created between two parallel plates of length 1m as shown in figure, (where m = mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of 2m/s. The angle of the deviation (

\theta

) of the path of the electron as it comes out of the field will be ……….

(A) $\tan^{-1}(4)$
(B) $\tan^{-1}(2)$
(C) $\tan^{-1}\left(\dfrac{1}{3}\right)$
(D) $\tan^{-1}(3)$

Q103·PhysicsSingle correctJEE Main 2022

A charge of 4 μC 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:

(A)1 μC and 3 μC
(B)2 μC and 2 μC
(C)0 and 4 μC
(D)1.5 μC and 2.5 μC

Q104·PhysicsNumericalJEE Main 2022

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}

m from its axis is ______

\mathrm{Vm}^{-1}

Q105·PhysicsNumericalJEE Main 2022

Three point charges of magnitude

5\mu C

,

0.16\mu C

and

0.3\mu C

are located at the vertices A, B, C of a right angled triangle whose sides are AB = 3cm,

BC = 3\sqrt{2}

cm and CA=3 cm and point A is the right angle corner. Charge at point A experiences ________ N of electrostatic force due to the other two charges.

Q106·PhysicsNumericalJEE Main 2022

The volume charge density of a sphere of radius 6 m is 2

\mu C

cm^{-3}

. The number of lines of force per unit surface area coming out from the surface of the sphere is _______

\times 10^{10}

NC^{-1}

. [Given : Permittivity of vacuum

\in_0 = 8.85 \times 10^{-12}

C^2

N^{-1} - m^{-2}

]

Q107·PhysicsSingle correctJEE Main 2022

A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength

1 \times 10^5

NC

^{-1}

. If the charge on the particle is 40 μC and the initial velocity is 200 ms

^{-1}

, how much distance it will travel before coming to the rest momentarily :

(A)1 m
(B)5 m
(C)10 m
(D)0.5 m

Q108·PhysicsSingle correctJEE Main 2022

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 :

(A) $x = d$
(B) $x = \frac{d}{2}$
(C) $x = \frac{d}{\sqrt{2}}$
(D) $x = \frac{d}{2\sqrt{2}}$

Q109·PhysicsSingle correctJEE Main 2022

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 comer D of the square, is :

(A) $\frac{q}{4\pi\epsilon_{0}a^{2}}\left(\frac{1}{\sqrt{2}} + \frac{1}{2}\right)$
(B) $\frac{q}{4\pi\epsilon_{0}a^{2}}\left(1 + \frac{1}{\sqrt{2}}\right)$
(C) $\frac{q}{4\pi\epsilon_{0}a^{2}}\left(1 - \frac{1}{\sqrt{2}}\right)$
(D) $\frac{q}{4\pi\epsilon_{0}a^{2}}\left(\frac{1}{\sqrt{2}} - \frac{1}{2}\right)$

Q110·PhysicsSingle correctJEE Main 2022

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 :

(A)Both statement-I and statement-II are true.
(B)Both statement-I and statement-I are false.
(C)Statement-I is true but statement-II is false.
(D)Statement-I is false but statement-II is true.

Q111·PhysicsSingle correctJEE Main 2022

Two point charges A and B of magnitude

+8\times10^{-6}

C and

-8\times10^{-6}

C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is

6.4\times10^4

NC

^{-1}

. The distance 'd' between the point charges A and B is:

(A)2.0 m
(B)3.0 m
(C)1.0 m
(D)4.0 m

Q112·PhysicsSingle correctJEE Main 2022

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 :

(A) $\dfrac{q}{\varepsilon_{0}}$
(B) $\dfrac{q}{2\varepsilon_{0}}$
(C) $\dfrac{q}{4\varepsilon_{0}}$
(D) $\dfrac{q}{2\pi\varepsilon_{0}}$

Q113·PhysicsSingle correctJEE Main 2022

Three identical charged balls each of charge 2C are suspended from a common point P by silk threads of 2m 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 :

(A)1 : 1
(B)1 : 4
(C) $\sqrt{3}$ : 2
(D) $\sqrt{3}$ : 1

Q114·PhysicsSingle correctJEE Main 2022

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

(A)1 : 4
(B)4 : 1
(C)1 : 8
(D)8 : 1

Q115·PhysicsSingle correctJEE Main 2022

In the figure, a very large plane sheet of positive charge is shown.

P_1

and

P_2

are two points at distance

l

and

2l

from the charge distribution. If σ is the surface charge density, then the magnitude of electric fields

E_1

and

E_2

at

P_1

and

P_2

respectively are :

(A) $E_1=\sigma/\varepsilon_0$ , $E_2=\sigma/2\varepsilon_0$
(B) $E_1=2\sigma/\varepsilon_0$ , $E_2=\sigma/\varepsilon_0$
(C) $E_1=E_2=\sigma/2\varepsilon_0$
(D) $E_1=E_2=\sigma/\varepsilon_0$

Q116·PhysicsSingle correctJEE Main 2022

Two identical charged particles each having a mass 10 g and charge

2.0\times10^{-7}

C area placed on a horizontal table with a separation of L between then 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}

]

(A)12 cm
(B)10 cm
(C)8 cm
(D)5 cm

Q117·PhysicsSingle correctJEE Main 2022

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 of the particle is :

(A) $\dfrac{\rho qR^{2}}{4\varepsilon_{0}}$
(B) $\dfrac{\rho qR^{2}}{2\varepsilon_{0}}$
(C) $\dfrac{q\rho}{4\varepsilon_{0}R^{2}}$
(D) $\dfrac{4\varepsilon_{0}R^{2}}{q\rho}$

Q118·PhysicsSingle correctJEE Main 2022

A vertical electric field of magnitude

4.9\times10^{5}

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/s

^{2}

)

(A) $1.6\times10^{-9}$ C
(B) $2.0\times10^{-9}$ C
(C) $3.2\times10^{-9}$ C
(D) $0.5\times10^{-9}$ C

Q119·PhysicsSingle correctJEE Main 2021

A cube is placed inside an electric field,

\vec{E} = 150y^{2}\hat{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 :

(A)3.8 × 10 $^{-11}$ C
(B)8.3 × 10 $^{-11}$ C
(C)3.8 × 10 $^{-12}$ C
(D)8.3 × 10 $^{-12}$ C

Q120·PhysicsSingle correctJEE Main 2021

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?

(A)At 5 cm from 20 $\mu$ C on the left side of system
(B)At 5 cm from $-$ 5 $\mu$ C on the right side
(C)At 1.25 cm from $-$ 5 $\mu$ C between two charges
(D)At midpoint between two charges

Q121·PhysicsSingle correctJEE Main 2021

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

(A)(c) and (d) only
(B)(b) and (d) only
(C)(d) only
(D)(a) and (c) only

Q122·PhysicsSingle correctJEE Main 2021

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 :-

(A) $E = \frac{\sigma}{2\varepsilon_0}\left(1 - \frac{Z}{(Z^2 + R^2)^{1/2}}\right)$
(B) $E = \frac{\sigma}{2\varepsilon_0}\left(1 + \frac{Z}{(Z^2 + R^2)^{1/2}}\right)$
(C) $E = \frac{2\varepsilon_0}{\sigma}\left(\frac{1}{(Z^2 + R^2)^{1/2}} + Z\right)$
(D) $E = \frac{\sigma}{2\varepsilon_0}\left(\frac{1}{(Z^2 + R^2)} + \frac{1}{Z^2}\right)$

Q123·PhysicsSingle correctJEE Main 2021

Figure shows a rod AB, which is bent in a 120° circular arc of radius R. A charge (−Q) is uniformly distributed over rod AB. What is the electric field

\vec{E}

at the centre of curvature O ?

(A) $\frac{3\sqrt{3}\,Q}{8\pi\varepsilon_{0}R^{2}}(\hat{i})$
(B) $\frac{3\sqrt{3}\,Q}{8\pi^{2}\varepsilon_{0}R^{2}}(\hat{i})$
(C) $\frac{3\sqrt{3}\,Q}{16\pi^{2}\varepsilon_{0}R^{2}}(\hat{i})$
(D) $\frac{3\sqrt{3}\,Q}{8\pi^{2}\varepsilon_{0}R^{2}}(-\hat{i})$

Q124·PhysicsSingle correctJEE Main 2021

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 'θ' with the vertical ?

(A) $x = \left( \frac{q^2 \ell}{2 \pi \varepsilon_0 mg} \right)^{1/2}$
(B) $x = \left( \frac{q^2 \ell}{2 \pi \varepsilon_0 mg} \right)^{1/3}$
(C) $x = \left( \frac{q^2 \ell^2}{2 \pi \varepsilon_0 m^2 g^2} \right)^{1/3}$
(D) $x = \left( \frac{q^2 \ell^2}{2 \pi \varepsilon_0 m^2 g} \right)^{1/3}$

Q125·PhysicsSingle correctJEE Main 2021

Two ideal electric dipoles A and B, having their dipole moment

p_1

and

p_2

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,

\frac{p_1}{p_2}

is : (take

\sin 37^\circ = \frac{3}{5}

)

(A) $\frac{3}{8}$
(B) $\frac{3}{2}$
(C) $\frac{4}{3}$
(D) $\frac{2}{3}$

Q126·PhysicsNumericalJEE Main 2021

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 change 'q'. If the free charged particle is displaced from its equilibrium position through distance 'x' (x << 1m). The particle executes SHM. Its angular frequency of oscillation will be ________

\times 10^5

rad /s if

q^2 = 10C^2

.

Q127·PhysicsSingle correctJEE Main 2021

An electric dipole is placed on x

-

axis in proximity to a line charge of linear density

3.0\times10^{-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 4 N is exerted on the dipole, find out the amount of positive charge of the dipole.

(A)0.485 mC
(B)8.8 μC
(C)815.1 nC
(D)4.44 μC

Q128·PhysicsNumericalJEE Main 2021

The total charge enclosed in an incremental volume of

2 \times 10^{-9}\,\mathrm{m^3}

located at the origin is ________ nC, if electric flux density of its field is found as

D = e^{-x}\sin y\,\hat{i} - e^{-x}\cos y\,\hat{j} + 2z\,\hat{k}

C/m

^2

.

Q129·PhysicsSingle correctJEE Main 2021

A certain charge Q is divided into 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 ?

(A) $Q = \frac{q}{2}$
(B) $Q = 4q$
(C) $Q = 2q$
(D) $Q = 3q$

Q130·PhysicsNumericalJEE Main 2021

A body having specific charge 8 μC / 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.

Q131·PhysicsNumericalJEE Main 2021

An infinite number of point charges, each carrying 1 μC charge, are placed along the y-axis at y = 1 m, 2 m, 4 m, 8 m.................. The total force on a 1 C point charge, placed at the origin, is x × 10

^{3}

N. The value of x, to the nearest integer, is________. [Take

\frac{1}{4\pi \epsilon_{0}}

= 9 × 10

^{9}

Nm

^{2}

/C

^{2}

]

Q132·PhysicsSingle correctJEE Main 2021

An oil drop of radius 2 mm with a density 3g cm

^{-3}

is held stationary under a constant electric field 3.55 × 10

^{5}

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/s

^{2}

)

(A)48.8 × 10 $^{11}$
(B)1.73 × 10 $^{10}$
(C)17.3 × 10 $^{10}$
(D)1.73 × 10 $^{12}$

Q133·PhysicsNumericalJEE Main 2021

The electric field in a region is given by

\vec{E} = \frac{2}{5}E_{0}\hat{i} + \frac{3}{5}E_{0}\hat{j}

with E

_{0}

= 4.0 × 10

^{3}

\frac{N}{C}

.The flux of this field through a rectangular surface area 0.4 m

^{2}

parallel to the Y − Z plane is _________Nm

^{2}

C

^{-1}

.

Q134·PhysicsSingle correctJEE Main 2021

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.

(A)0.424 nC m $^{-2}$
(B)47.88 C/m
(C)0.07 nC m $^{-2}$
(D)4.0 nC m $^{-2}$

Q135·PhysicsSingle correctJEE Main 2021

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 =

\frac{\sqrt{3}}{2}

L .

(A) $\frac{Q}{2\sqrt{3}\pi\varepsilon_0 L^{2}}$
(B) $\frac{\sqrt{3}Q}{4\pi\varepsilon_0 L^{2}}$
(C) $\frac{Q}{3\pi\varepsilon_0 L^{2}}$
(D) $\frac{Q}{4\pi\varepsilon_0 L^{2}}$

Q136·PhysicsSingle correctJEE Main 2021

Given below are two statements : Statement – I : An electric dipole is placed at the centre of a hollow sphere. The flux of 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 theelectric flux passing through this closed spherical surface of radius r is not zero. In the light of the above statements. Choose the correct answerfrom the option given below :

(A)Statement I is true but Statement II is false
(B)Statement I is false but Statement II is true
(C)Both Statement I and Statement II are true
(D)Both Statement I and Statement II are false

Q137·PhysicsNumericalJEE Main 2021

The electric field in a region is given by

\vec{E} = \left(\dfrac{3}{5}E_0\hat{i} + \dfrac{4}{5}E_0\hat{j}\right)\dfrac{N}{C}

. The ratio of flux of reported field through the rectangular surface of area 0.2

m^2

(parallel to y-z plane) to that of the surface of area 0.3

m^2

(parallel to x-z plane) is a : b, where a = __________ [Here

\hat{i}

,

\hat{j}

and

\hat{k}

are unit vectors along x, y and z-axes respectively]

Q138·PhysicsNumericalJEE Main 2021

Two identical conducting spheres with negligible volume have 2.1nC and -0.1nC 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 _______× 10

^{-9}

N. 1 [Given : 4πε

_{0}

=9×10

_{9}

SI unit]

Q139·PhysicsSingle correctJEE Main 2021

An electron with kinetic energy K1 enters between parallel plates of a capacitor at an angle 'α’ with the plates. It leaves the plates at angle 'β' with kinetic energy K2. Then the ratio of kinetic energies K1 : K2 will be:

(A)cossin $^{2}^{2}$ βα
(B)coscos $^{2}^{2}$ αβ
(C)cossinαβ
(D)coscosαβ

Q140·PhysicsSingle correctJEE Main 2021

A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field E though the shaded area is: Z qY X qqqq

(A) $\dfrac{q}{48\varepsilon_{0}}$
(B) $\dfrac{q}{8\varepsilon_{0}}$
(C) $\dfrac{q}{24\varepsilon_{0}}$
(D) $\dfrac{q}{4\varepsilon_{0}}$

Q141·PhysicsNumericalJEE Main 2021

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 . Then charge on each of the sphere is a×10

^{-}

^{8}

C. The value of 'a' will be________. 21

Q142·PhysicsSingle correctJEE Main 2021

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)

(A) $\left(\dfrac{q^{2}}{2\pi\varepsilon_{0}md^{3}}\right)^{\frac{1}{2}}$
(B) $\left(\dfrac{\pi\varepsilon_{0}md^{3}}{2q^{2}}\right)^{\frac{1}{2}}$
(C) $\left(\dfrac{2\pi\varepsilon_{0}md^{3}}{q^{2}}\right)^{\frac{1}{2}}$
(D) $\left(\dfrac{2q^{2}}{\pi\varepsilon_{0}md^{3}}\right)^{\frac{1}{2}}$

Q143·PhysicsSingle correctJEE Main 2021

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 :

(A) $\frac{2Q}{3\sqrt{3}\pi\varepsilon_0 a^2}\left(\hat{x}+\hat{y}+\hat{z}\right)$
(B) $\frac{Q}{3\sqrt{3}\pi\varepsilon_0 a^2}\left(\hat{x}+\hat{y}+\hat{z}\right)$
(C) $\frac{-2Q}{3\sqrt{3}\pi\varepsilon_0 a^2}\left(\hat{x}+\hat{y}+\hat{z}\right)$
(D) $\frac{-Q}{3\sqrt{3}\pi\varepsilon_0 a^2}\left(\hat{x}+\hat{y}+\hat{z}\right)$

Q144·PhysicsNumericalJEE Main 2021

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 10^{3}

Nm

^{2}

/C.

Q145·PhysicsMultiple correctJEE Advanced 2020

Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is

\alpha

. The spheres are now immersed in a dielectric liquid of density

800\ \text{kg m}^{-3}

and dielectric constant 21. If the angle between the strings remains the same after the immersion, then

(A)electric force between the spheres remains unchanged
(B)electric force between the spheres reduces
(C)mass density of the spheres is $840\ \text{kg m}^{-3}$
(D)the tension in the strings holding the spheres remains unchanged

Q146·PhysicsIntegerJEE Advanced 2020

Two large circular discs separated by a distance of 0.01 m are connected to a battery via a switch as shown in the figure. Charged oil drops of density

900\ \text{kg m}^{-3}

are released through a tiny hole at the center of the top disc. Once some oil drops achieve terminal velocity, the switch is closed to apply a voltage of 200 V across the discs. As a result, an oil drop of radius

8 \times 10^{-7}

m stops moving vertically and floats between the discs. The number of electrons present in this oil drop is _________. (neglect the buoyancy force, take acceleration due to gravity

= 10\ \text{ms}^{-2}

and charge on an electron (e)

= 1.6 \times 10^{-19}

C)

Q147·PhysicsNumericalJEE Advanced 2020

A circular disc of radius

R

carries surface charge density

\sigma(r) = \sigma_0\left(1 - \frac{r}{R}\right)

, where

\sigma_0

is a constant and

r

is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is

\phi_0

. Electric flux through another spherical surface of radius

\frac{R}{4}

and concentric with the disc is

\phi

. Then the ratio

\frac{\phi_0}{\phi}

is_________.

Q148·PhysicsMultiple correctJEE Advanced 2020

A uniform electric field,

\vec{E} = -400\sqrt{3}\hat{y}

NC^{-1}

is applied in a region. A charged particle of mass m carrying positive charge q is projected in this region with an initial speed of

2\sqrt{10} \times 10^{6}

ms^{-1}

. This particle is aimed to hit a target T, which is 5 m away from its entry point into the field as shown schematically in the figure. Take

\frac{q}{m} = 10^{10}

Ckg^{-1}

. Then-

(A)the particle will hit T if projected at an angle 45º from the horizontal
(B)the particle will hit T if projected either at an angle 30º or 60º from the horizontal
(C)time taken by the particle to hit T could be $\sqrt{\frac{5}{6}}$ μs as well as $\sqrt{\frac{5}{2}}$ μs
(D)time taken by the particle to hit T is $\sqrt{\frac{5}{3}}$ μs

Q149·PhysicsSingle correctJEE Main 2020

Charge

Q_1

and

Q_2

are at point A and B of a right angle triangle OAB (see figure). The resultant electric field at point O is perpendicular to the hypotenuse, then

\dfrac{Q_1}{Q_2}

is proportional to:

(A) $\dfrac{x_1^{3}}{x_2^{3}}$
(B) $\dfrac{x_2}{x_1}$
(C) $\dfrac{x_1}{x_2}$
(D) $\dfrac{x_2^{2}}{x_1^{2}}$

Q150·PhysicsSingle correctJEE Main 2020

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?

(A) $F = \frac{1}{4\pi ∈_{0}}\frac{Qq}{R^{2}}$ for $r < R$
(B) $\frac{1}{4\pi ∈_{0}}\frac{qQ}{R^{2}} > F > 0$ for $r < R$
(C) $F = \frac{1}{4\pi ∈_{0}}\frac{Qq}{r^{2}}$ for $r > R$
(D) $F = \frac{1}{4\pi ∈_{0}}\frac{Qq}{r^{2}}$ for all r

Q151·PhysicsSingle correctJEE Main 2020

A particle of charge q and mass m is subjected to an electric field

E = E_0(1 - ax^{2})

in the x-direction, where a and

E_0

are constants. Initially the particle was at rest at

x = 0

. Other then the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is:

(A) $\sqrt{\frac{3}{a}}$
(B) $\sqrt{\frac{1}{a}}$
(C)a
(D) $\sqrt{\frac{2}{a}}$

Q152·PhysicsSingle correctJEE Main 2020

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.

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q153·PhysicsSingle correctJEE Main 2020

Consider a sphere of radius R which carries a uniform charge density

\rho

. If a sphere of radius

\dfrac{R}{2}

is carved out of it, as shown the ratio

\dfrac{|\vec{E}_{A}|}{|\vec{E}_{B}|}

of magnitude of electric field

\vec{E}_{A}

and

\vec{E}_{B}

, respectively, at point A and B due to the remaining portion is:

(A) $\dfrac{18}{34}$
(B) $\dfrac{17}{54}$
(C) $\dfrac{18}{54}$
(D) $\dfrac{21}{34}$

Q154·PhysicsNumericalJEE Main 2020

An electric field

\vec{E}=4x\hat{i}-(y^{2}+1)\hat{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 (

\phi_{I}-\phi_{II}

) is (in N m

^{2}

/C) __________.

Q155·PhysicsSingle correctJEE Main 2020

An electric dipole of moment

\vec{p} = (-\hat{i} - 3\hat{j} + 2\hat{k}) \times 10^{-29}

cm is at the origin (0, 0, 0). The electric field due to this dipole at

\vec{r} = +\hat{i} + 3\hat{j} + 5\hat{k}

(note that

\vec{r} \cdot \vec{p} = 0

) is parallel to:

(A) $(-\hat{i} - 3\hat{j} + 2\hat{k})$
(B) $(+\hat{i} - 3\hat{j} - 2\hat{k})$
(C) $(-\hat{i} + 3\hat{j} - 2\hat{k})$
(D) $(+\hat{i} + 3\hat{j} - 2\hat{k})$

Q156·PhysicsSingle correctJEE Main 2020

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)

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q157·PhysicsSingle correctJEE Main 2020

Three charged particles 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:

(A) $\dfrac{2\sqrt{3}q}{\pi\varepsilon_{0}d^{2}}$
(B) $\dfrac{\sqrt{3}q}{\pi\varepsilon_{0}d^{2}}$
(C) $\dfrac{3\sqrt{3}q}{4\pi\varepsilon_{0}d^{2}}$
(D) $\dfrac{\sqrt{3}q}{4\pi\varepsilon_{0}d^{2}}$

Q158·PhysicsSingle correctJEE Main 2020

In finding the electric field using Gauss law the formula

|\vec{E}| = \dfrac{q_{enc}}{\varepsilon_{0}|A|}

is applicable. In the formula

\varepsilon_0

is permittivity of free space, A is the area of Gaussain surface and

q_{enc}

is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation? Only when the Gaussian surface is an

(A)equipotential surface and $|\vec{E}|$ is constant on the surface.
(B)For any choice of Gaussian surface.
(C)Only when $|\vec{E}|$ = constant on the surface.
(D)Only when the Gaussian surface is an equipotential surface.

Q159·PhysicsSingle correctJEE Main 2020

Two infinite planes each with uniform surface charge density

+\sigma

are kept in such a way that the angle between them is 30°. The electric field in the region shown between them is given by:

(A) $\dfrac{\sigma}{2\varepsilon_0}\left[\left(1-\dfrac{\sqrt{3}}{2}\right)\hat{y}-\dfrac{\hat{x}}{2}\right]$
(B) $\dfrac{\sigma}{2\varepsilon_0}\left[\left(1+\sqrt{3}\right)\hat{y}-\dfrac{\hat{x}}{2}\right]$
(C) $\dfrac{\sigma}{2\varepsilon_0}\left[\left(1+\sqrt{3}\right)\hat{y}+\dfrac{\hat{x}}{2}\right]$
(D) $\dfrac{\sigma}{\varepsilon_0}\left[\left(1+\dfrac{\sqrt{3}}{2}\right)\hat{y}+\dfrac{\hat{x}}{2}\right]$

Q160·PhysicsMultiple correctJEE Advanced 2019

A charged shell of radius R carries a total charge Q. Given φ as the flux of electric field through a closed cylindrical surface of height h, radius r and with its center same as that of the shell. Here, center of the cylinder is a point on the axis of the cylinder which is equidistant from its top and bottom surfaces. Which of the following option(s) is/are correct? [

\varepsilon_0

is permittivity of free space]

(A)If h < 8R/5 and r = 3R/5 then φ = 0
(B)If h > 2R and r > R then φ = Q/ $\varepsilon_0$
(C)If h > 2R and r = 4R/5 then φ = Q/ $5\varepsilon_0$
(D)If h > 2R and r = 3R/5 then φ = Q/ $5\varepsilon_0$

Q161·PhysicsSingle correctJEE Main 2019

Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by r(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 :

(A) $a = \dfrac{3R}{2^{1/4}}$
(B) $a = 2^{-1/4}R$
(C) $a = 8^{-1/4}R$
(D) $a = R/\sqrt{3}$

Q162·PhysicsSingle correctJEE Main 2019

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

\vec{P}

as shown. In this case :

(A)Surface charge density on the inner surface of the shell is zero everywhere.
(B)Electric field outside the shell is the same as that of a point charge at the centre of the shell.
(C)Surface charge density on the inner surface is uniform and equal to $\dfrac{(Q/2)}{4\pi a^{2}}$
(D)Surface charge density on the outer surface depends on $|\vec{P}|$

Q163·PhysicsSingle correctJEE Main 2019

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 vary as:

(A) $E \propto \dfrac{1}{D}$
(B) $E \propto \dfrac{1}{D^{3}}$
(C) $E \propto \dfrac{1}{D^{2}}$
(D) $E \propto \dfrac{1}{D^{4}}$

Q164·PhysicsSingle correctJEE Main 2019

The bob of a simple pendulum has mass 2g and a charge of

5.0\mu C

. It is at rest in a uniform horizontal electric field of intensity

2000\dfrac{V}{m}

. At equilibrium, the angle that the pendulum makes with the vertical is: (take

g=10\dfrac{m}{s^2}

)

(A) $\tan^{-1}(2.0)$
(B) $\tan^{-1}(0.2)$
(C) $\tan^{-1}(5.0)$
(D) $\tan^{-1}(0.5)$

Q165·PhysicsSingle correctJEE Main 2019

Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure:

(A) $\sqrt{3}\, q\ell \frac{\hat{j} - \hat{i}}{\sqrt{2}}$
(B) $(q\ell)\frac{\hat{i} + \hat{j}}{\sqrt{2}}$
(C) $2q\ell \hat{j}$
(D) $-\sqrt{3}\, q\ell \hat{j}$

Q166·PhysicsSingle correctJEE Main 2019

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

(A)-Q/4
(B)+Q/2
(C)+Q/4
(D)-Q/2

Q167·PhysicsSingle correctJEE Main 2019

Two point charges

q_1(\sqrt{10}\ \mu C)

and

q_2(-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,

\left[\text{take } \frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}\ Nm^{2}C^{-2}\right]

(A) $(63\hat{i} - 27\hat{i}) \times 10^{2}$
(B) $(-63\hat{i} + 27\hat{i}) \times 10^{2}$
(C) $(81\hat{i} - 81\hat{i}) \times 10^{2}$
(D) $(-81\hat{i} + 81\hat{i}) \times 10^{2}$

Q168·PhysicsSingle correctJEE Main 2019

For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its centre. Then value of h is:

(A) $\dfrac{R}{\sqrt{5}}$
(B) $\dfrac{R}{\sqrt{2}}$
(C)R
(D) $R\sqrt{2}$

Q169·PhysicsSingle correctJEE Advanced 2018

The electric field E is measured at a point P(0, 0, d) generated due to various charge distributions and the dependence of E on d is found to be different for different charge distributions. List-I contains different relations between

E

and d. List-II describes different electric charge distributions, along with their locations. Match the functions in List-I with the related charge distributions in List-II.

LIST-I	LIST-II
P.E is independent of d	1.A point charge Q at the origin
Q. $E \propto \dfrac{1}{d}$	2.A small dipole with point charges Q at $(0, 0, \ell)$ and $-Q$ at $(0, 0, -\ell)$ . Take $2\ell \ll d$
R. $E \propto \dfrac{1}{d^{2}}$	3.An infinite line charge coincident with the x-axis, with uniform linear charge density $\lambda$
S. $E \propto \dfrac{1}{d^{3}}$	4.Two infinite wires carrying uniform linear charge density parallel to the x- axis. The one along $(y = 0, z = \ell)$ has a charge density $+\lambda$ and the one along $(y = 0, z = -\ell)$ has a charge density $-\lambda$ . Take $2\ell << d$
	5.Infinite plane charge coincident with the xy-plane with uniform surface charge density

(A)P $\rightarrow$ 5; Q $\rightarrow$ 3, 4; R $\rightarrow$ 1; S $\rightarrow$ 2
(B)P $\rightarrow$ 5; Q $\rightarrow$ 3; R $\rightarrow$ 1, 4; S $\rightarrow$ 2
(C)P $\rightarrow$ 5; Q $\rightarrow$ 3; R $\rightarrow$ 1, 2; S $\rightarrow$ 4
(D)P $\rightarrow$ 4; Q $\rightarrow$ 2, 3; R $\rightarrow$ 1; S $\rightarrow$ 5

Q170·PhysicsNumericalJEE Advanced 2018

A particle, of mass

10^{-3}

kg and charge 1.0 C, is initially at rest. At time t = 0, the particle comes under the influence of an electric field

\vec{E}(t) = E_{0}\sin\omega t\,\hat{i}

, where

E_{0} = 1.0

NC

^{-1}

and

\omega = 10^{3}

rad s

^{-1}

. Consider the effect of only the electrical force on the particle. Then the maximum speed, in m s

^{-1}

, attained by the particle at subsequent times is ____________.

Q171·PhysicsMultiple correctJEE Advanced 2018

An infinitely long thin non-conducting wire is parallel to the z-axis and carries a uniform line charge density

\lambda

. It pierces a thin non-conducting spherical shell of radius

R

in such a way that the arc

PQ

subtends an angle

120^{\circ}

at the centre

O

of the spherical shell, as shown in the figure. The permittivity of free space is

\varepsilon_{0}

. Which of the following statements is (are) true?

(A)The electric flux through the shell is $\sqrt{3}R\lambda/\varepsilon_{0}$
(B)The z-component of the electric field is zero at all the points on the surface of the shell
(C)The electric flux through the shell is $\sqrt{2}R\lambda/\varepsilon_{0}$
(D)The electric field is normal to the surface of the shell at all points

Q172·PhysicsMultiple correctJEE Advanced 2017

A point charge

+Q

is placed just outside an imaginary hemispherical surface of radius R as shown in the figure. Which of the following statements is/are correct?

(A)The electric flux passing through the *curved* surface of the hemisphere is $-\dfrac{Q}{2\varepsilon_{0}}\left(1 - \dfrac{1}{\sqrt{2}}\right)$
(B)Total flux through the curved and the flat surfaces is $\dfrac{Q}{\varepsilon_{0}}$
(C)The component of the electric field normal to the flat surface is constant over the surface
(D)The circumference of the flat surface is an equipotential

Q173·PhysicsSingle correctJEE Advanced 2016

Consider an evacuated cylindrical chamber of height h having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius r << h. Now a high voltage source (HV) is connected across the conducting plates such that the bottom plate is at

+V_{0}

and the top plate at

-V_{0}

. Due to their conducting surface, the balls will get charged, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity) Which one of the following statements is correct?

(A)The balls will bounce back to the bottom plate carrying the opposite charge they went up with
(B)The balls will execute simple harmonic motion between the two plates
(C)The balls will bounce back to the bottom plate carrying the same charge they went up with
(D)The balls will stick to the top plate and remain there

Q174·PhysicsSingle correctJEE Advanced 2016

Consider an evacuated cylindrical chamber of height h having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius r << h. Now a high voltage source (HV) is connected across the conducting plates such that the bottom plate is at

+V_{0}

and the top plate at

-V_{0}

. Due to their conducting surface, the balls will get charged, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity) The average current in the steady state registered by the ammeter in the circuit will be

(A)proportional to $V_{0}^{1/2}$
(B)proportional to $V_{0}^{2}$
(C)proportional to the potential $V_{0}$
(D)zero

Q175·PhysicsMultiple correctJEE Advanced 2015

Consider a uniform spherical charge distribution of radius

R_{1}

centred at the origin O. In this distribution, a spherical cavity of radius

R_{2}

, centred at P with distance

OP = a = R_{1} - R_{2}

(see figure) is made. If the electric field inside the cavity at position

\vec{r}

is

\vec{E}(\vec{r})

, then the correct statement(s) is(are)

(A) $\vec{E}$ is uniform, its magnitude is independent of $R_{2}$ but its direction depends on $\vec{r}$
(B) $\vec{E}$ is uniform, its magnitude depends on $R_{2}$ and its direction depends on $\vec{r}$
(C) $\vec{E}$ is uniform, its magnitude is independent of $a$ but its direction depends on $\vec{a}$
(D) $\vec{E}$ is uniform and both its magnitude and direction depend on $\vec{a}$

Q176·PhysicsMultiple correctJEE Advanced 2015

The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density

\lambda

are kept parallel to each other. In their resulting electric field, point charges

q

and

-q

are kept in equilibrium between them. The point charges are confined to move in the x direction only. If they are given a small displacement about their equilibrium positions, then the correct statement(s) is(are)

(A)Both charges execute simple harmonic motion.
(B)Both charges will continue moving in the direction of their displacement.
(C)Charge $+q$ executes simple harmonic motion while charge $-q$ continues moving in the direction of its displacement.
(D)Charge $-q$ executes simple harmonic motion while charge $+q$ continues moving in the direction of its displacement.

Q177·PhysicsIntegerJEE Advanced 2015

An infinitely long uniform line charge distribution of charge per unit length

\lambda

lies parallel to the y-axis in the y-z plane at

z = \dfrac{\sqrt{3}}{2}a

(see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its center at the origin is

\dfrac{\lambda L}{n\varepsilon_{0}}

(

\varepsilon_{0}

= permittivity of free space), then the value of

n

is

Q178·PhysicsMultiple correctJEE Advanced 2014

Let

E_1(r)

,

E_2(r)

and

E_3(r)

be the respective electric fields at a distance

r

from a point charge

Q

, an infinitely long wire with constant linear charge density

\lambda

, and an infinite plane with uniform surface charge density

\sigma

. If

E_1(r_0) = E_2(r_0) = E_3(r_0)

at a given distance

r_0

, then

(A) $Q = 4\sigma\pi r_0^2$
(B) $r_0 = \frac{\lambda}{2\pi\sigma}$
(C) $E_1(r_0/2) = 2E_2(r_0/2)$
(D) $E_2(r_0/2) = 4E_3(r_0/2)$

Q179·PhysicsSingle correctJEE Advanced 2014

Charges

Q

,

2Q

and

4Q

are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii

R/2

,

R

and

2R

respectively, as shown in figure. If magnitudes of the electric fields at point P at a distance

R

from the centre of spheres 1, 2 and 3 are

E_{1}

,

E_{2}

and

E_{3}

respectively, then

(A) $E_{1} > E_{2} > E_{3}$
(B) $E_{3} > E_{1} > E_{2}$
(C) $E_{2} > E_{1} > E_{3}$
(D) $E_{3} > E_{2} > E_{1}$

Q180·PhysicsSingle correctJEE Advanced 2014

Four charges

Q_{1}

,

Q_{2}

,

Q_{3}

and

Q_{4}

of same magnitude are fixed along the

x

axis at

x = -2a

,

-a

,

+a

and

+2a

, respectively. A positive charge

q

is placed on the positive

y

axis at a distance

b > 0

. Four options of the signs of these charges are given in List I. The direction of the forces on the charge

q

is given in List II. Match List I with List II and select the correct answer using the code given below the lists.

List I	List II
P. $Q_{1}$ , $Q_{2}$ , $Q_{3}$ $Q_{4}$ all positive	1. $+x$
Q. $Q_{1}$ , $Q_{2}$ positive; $Q_{3}$ , $Q_{4}$ negative	2. $-x$
R. $Q_{1}$ , $Q_{4}$ positive ; $Q_{2}$ , $Q_{3}$ negative	3. $+y$
S. $Q_{1}$ , $Q_{3}$ positive; $Q_{2}$ , $Q_{4}$ negative	4. $-y$

(A)P-3, Q-1, R-4, S-2
(B)P-4, Q-2, R-3, S-1
(C)P-3, Q-1, R-2, S-4
(D)P-4, Q-2, R-1, S-3

Q181·PhysicsMultiple correctJEE Advanced 2013

Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities

\rho_{1}

and

\rho_{2}

respectively, touch each other. The net electric field at a distance 2R from the centre of the smaller sphere, along the line joining the centre of the spheres is zero. The ratio

\rho_{1}/\rho_{2}

can be

(A) $-4$
(B) $-\frac{32}{25}$
(C) $\frac{32}{25}$
(D) $4$

Q182·PhysicsMultiple correctJEE Advanced 2013

Two non-conducting spheres of radii

R_{1}

and

R_{2}

and carrying uniform volume charge densities

+\rho

and

-\rho

, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,

(A)the electrostatic field is zero
(B)the electrostatic potential is constant
(C)the electrostatic field is constant in magnitude
(D)the electrostatic field has same direction

Electric Field and Coulomb's Law — JEE Previous Year Questions

All 182 Electric Field and Coulomb's Law questions

Electric Field and Coulomb's Law — frequently asked

How many questions from Electric Field and Coulomb's Law appear in JEE?

Is Electric Field and Coulomb's Law an important chapter for JEE?

Where do these Electric Field and Coulomb's Law questions come from?

Other Physics chapters

Practise Electric Field and Coulomb's Law until it stops costing you marks.